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I need to know that a universal law like the First Law Of Motion may be disproved or not. I mean, that how can we make sure that the particular law will hold true at all places of the universe?

'Disproving' means showing that something is not true. The name for showing that a law will hold true at all places and times 'proving'.

Many philosophers would say the answer is yes:

https://plato.stanford.edu/entries/induction-problem/

In reality, proof and disproof are both impossible, as explained by the philosopher Karl Popper. Any argument uses assumptions and ideas about the consequences of those assumptions. The truth of the conclusion of any argument depends on the correctness of the assumptions and of the rules applied to them. Trying to guarantee the truth of the assumptions and rules would involve making another argument with more assumptions that would have to be proved. So arguments are useless for proving any statement, including the statement that an idea is false.

But it is still possible to learn about how the world works. If we assume some universal law is true and try to check its consequences and we find a clash between the results of the check and the consequences of the law then there is a problem somewhere in the set of ideas involved in the check. One possibility is that the law is wrong. Another possibility is that the check is flawed in some way. We might also have made a mistake about the consequences of the law. To solve this problem we come up with explanations of the clash and try to test the explanations until we find one that solve the original problem and has no other known problems.

For more explanations of these ideas, see the material here:

http://fallibleideas.com/books#popper

Some commenters on this answer seem to think that disproof is both possible and required for science. They are wrong on both counts. First, you can't prove an observational statement, as Popper noted in "Logic of Scientific Discovery" Section 25:

Every description uses universal names (or symbols, or ideas); every statement has the character of a theory, of a hypothesis. The statement, ‘Here is a glass of water’ cannot be verified by any observational experience. The reason is that the universals which appear in it cannot be correlated with any specific sense-experience. (An ‘immediate experience’ is only once ‘immediately given’; it is unique.) By the word ‘glass’, for example, we denote physical bodies which exhibit a certain law-like behaviour, and the same holds for the word ‘water’. Universals cannot be reduced to classes of experiences; they cannot be ‘constituted’.

See also "The Beginning of Infinity" by David Deutsch chapter 2. Since no observational statement can be proved, and such proof would be required to disprove a theory, theories can't be disproved.

Disproof is also not required. Rather, you have a conjectured physical law and a conjectured observation that are judged to be incompatible. This constitutes a problem independent of whether the observation or the alleged incompatibility are correct. And if you want to understand the world you have to resolve the incompatibility, perhaps by rejecting a conjectured law, or, sometimes, by rejecting a conjectured observation.

We can't "make sure that the particular law will hold true at all places of the universe", and it is not possible to do so without deity-like omniscience.

Proof belongs to the domain of logic and mathematics, where there can be no question of the accuracy of a given abstraction, because the subjects are the manipulation of abstractions.

But the example of a universal law you give belongs to science, which deals only in evidence, and probabilities. Consider the Problem Of Induction, which can only be answered by something like Bayesian statistics, likelihood based on experience.

It is generally poorly understood that the idea of a law, only proceeds from analogy with legal systems, and that is a bad analogy. We make abstractions of the world, often as much for tractability as accuracy, and then compare outputs to the world - but the world always has the final say. See Nancy Cartwright's How The Laws of Physics Lie for more on this.

So you might reasonably ask, what is the most universal? How universal a principle or model or framework can we get? Not easy to answer, because even just within physics there are many modes and methodologies, and comparing them for universality is more opinion than science. Candidates might be Noether's Theorem, which links symmetries in dimensions to conservation laws. Einstein said he felt thermodynamics to be more fundamental than quantum mechanics or relativity, and developments in entropic gravity seem like they are supporting that, as well as linking to Wheeler's 'It From Bit' doctrine of the fundamental reality only of information.

But just like Newton's Laws break down at high speeds and small scales, QM & relativity break down at black holes - even our most universal explanations find gaps & exceptions where they break down. What happened before the big bang if the dimension of time only came into existence then?

There are theories that the speed of light might have varied across time, or other fundamental constants might vary across space. The universe is full of uncertainties, not universalities..!

The short answer is that we cannot be 100% certain for all cases. We can be more certain for the "frames" where we can do experiments, but the further off we go from actual experiments it gets less and less certain. We know for certain that Newtons laws are false by doing experiments proving them false.

Generally, it is much easier to find one example proving that a theory is wrong than showing that there is not any example (remember, abscense of proof is not proof of abscense)

Today scientists do not call their theories for laws for a good reason. The simple experience is that sooner or later there will be some circumstance that proves the law false (well, as far as we currently guess this probably goes for all our physics theories). Any theory we have, including Newtons so called laws, can only be shown to be valid in a certain "frame" surrounding it. Outside that frame it might be correct, or not. The frame in physics is most often considered as doing experiments. (Theories that cannot be proved either wrong or right are generally frowned upon).

Several of Newtons laws were proved wrong in the case of relativity (Einstein). Law one gets invalidated in a frame known as quantuum mechanics (which is very strange animal if you ask me but experiments shows that it is a better explanation than Newtons laws for small things).

So can we really be sure that things are the same everywhere and all the time. Scientist do spend lifetimes trying to answer that question. Basically the jury is not out yet: has the constants of cosmology changed over time (except from during big bang, the answer currently seems to be no). Speed of light, the fine constant and so on, currently seems to not have changed over time, and probably not over distance either. But we cannot really be 100% certain right now. Probably never, so don´t expect any new laws. But then who knows?

Yeah, you just make an observation where the law is being broken, and then the situation in which you made the observations is recreated and scrutinized to make sure what you observed was correct. Then you get a special case where the law doesn't hold true. Descriptive laws aren't logical axioms, they're empirical observations.

The process is pretty straight forward. Also, we haven't observed the entire universe and we haven't fully analyzed what we can observe. The laws holding true 100% of the time is purely theoretical. For all we know black holes and dark matter actually just break the first law of motion. I don't think there's any evidence of that, but it could be the case. It's nothing to be worried about. What we have now is good enough for our predictive models and not easily disproved.

Of course they can be disproved. That is why they are called theoretical. Or perhaps I should not say disproved but rather appended. You use the first law of motion as an example, and that example is logical, but there must be some other way to calculate motion and it’s effects. But so far no one has exhausted themselves to look beyond what is offered as law. Here is a fundamental deficiency in intellect, that we accept to know what is told to us more than we desire to find the answers for ourselves. Leibniz stated in some form, ‘that if you are to solve a problem you must learn from the bottom up and understand each concept yourself no matter how basic’. If one puts their philosophical mind to use beyond the parameters defined for them, one can see a world of possibilities. Is that not what philosophy really is?

Please note Newton's first law of motion.

"Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force."

I don't know whether there is any other version to this law.

A living object is also an object. If so, which is the force that moves and stops a living object? Is it purely external?

What all forces stop an egg that is rolling on the floor? I think the internal force also has its influence in stopping the egg. You may argue that an egg is an amassed form of different substances...or the jelly-like-fluid that exerts friction is also attracted by the earth. So you may say that force also is external. But we cannot ignore the fact that the jelly-like-fluid (both egg yolk and egg white) also attracts the earth. Then the force that stops a rolling egg must be internal and external. Similarly you may imagine a jelly-like-ball (a homogeneous substance) that rolls on the floor. What all forces stop its rolling?

What I am trying to say is that the last term ('eternal force') in the law would need to be rectified if scientists discovered that the characteristics of force within the tiniest particles...I mean, if particles are also jelly-like.

Actually I have no reference to put forward. This is just a possibility in this material world..."If scientists discover so, a rectification would be needed in the law."

We need not go outer space to disprove some Universal Laws because the laws that are known as Universal laws are not created after they realized the Universe.

When science realizes the meaninglessness of internal and external, the aforesaid law will be disproved. In course of time Science will disprove it theoretically. And when someone realizes it he will understand that it was not just a theory.

For details: http://www.fusw.org/uploads/1/3/0/4/13041662/corners_of_truth_~_hinduism.pdf