If there are no doubt-free areas in Science, then it is Nihilism. Nihilism is not true, and not right, because rejects the existence of Absolute Truth.
I'm pretty sure not a single statement in that was correct.
The only "doubt free" areas are simple observations (and even they can be taken to have some doubt as soon as it becomes recollection).
Other things are just beyond any reasonable doubt.
Nihilism comes in many forms, but the basic idea is that you know that you exist, but can't be certain of anything else.
There are lesser versions like existential nihilism which simply accepts that life does not have an objective meaning; and moral nihilism which rejects objective moral values.
That is completely separate from science, even what you presented it as.
So no, Nihilism is not science.
Absolute truth is simply anything which is true which is impossible to not be true, for example, a square has 4 sides, a square circle cannot exist, and so on.
Nihilism doesn't reject absolute truth.
Or by "absolute truth" did you mean the garbage you presented as absolute truth before?
If so yes, nihilism would typically reject your absolute truths, like "pixies are real", but so does almost every sane person.
The theories are true in own area of applicability, thus, the Newton Physics was never made false.
Who said anything about Newtonian (I assume that is what you mean) Physics being false?
Again, falsifiable doesn't mean false.
Look the official definition of Truth:
https://simple.wikipedia.org/wiki/Absolute_truth
That is an encyclopedia, not a dictionary. That is also for the phrase absolute truth, not truth.
Absolute truth is a subset of truth.
To put it simply, an absolute truth is any truth which is absolute (i.e. not subject to anything, other than definitions).
For example, "a square has 4 sides" is an absolute truth. That is because nothing can change the truth value of that statement because by definition a square is a quadrilateral and thus it has 4 sides.
A non absolute truth would be something like "it is 7:12 am".
It may be true for a particular time zone at a particular time, and thus is true, but it is subject to the timezone and the time, and thus won't be true soon or in other locations.