The film is based ion the common idea that language modifies the way we perceive the reality.

In this sense, we think of things being "based" on top of a surface, like a brick placed on the ground. So "on". You could have said "rooted in the idea" - there the image is more like a tree that has grown roots *into* the ground, penetrated it.

"reality" is uncountable, so "the reality" suggests that there are many, and you want to pick out one in particular. Like "water is wet" vs "the water (in this lake) is very cold".

The idea of there being many realities isn't so strange when you watch films like Arrival :) but it sounds more natural here to speak like there's only our reality.

The trueth of this claim seems clear.

For every person who has had to deal with a new language it's obvious that some features of the other language compel him/her to think in a different way.

"him/her" is awkward - you would probably use "generic you", like I just did. They compel you to think in a different way.

Sometimes I feel the differences are ion the surface, whereas the reality's fabric stays the same; but there are other times, at which I feel as if I were having a brand new experience about a thing known long time ago.

Or "known _a_ long time ago". Not sure of the grammar for that. I guess because one's only an adverb and the other has a noun.

"on" vs "in" again. A surface is a two dimensional plane, it has no depth, so it sounds a little odd to say something is "in" it.