So, special relativity says that every frame is as good as any other frame, and there is no absolute frame of reference. All good.
And special relativity is experimentally falsified and general relativity uses the word general to cover the case when inertial frames are only local and not global, such as in the universe we live in.
Suppose there is a finite universe (let's just assume the universe is not expanding), so it has boundaries,
You can have a finite universe unexpanding without boundaries. Might not be stable and so might start collapsing locally. But the point is your assumption hat finite means has boundary is a false conclusion.
so theoretically, a person can determine his position and absolute velocity in the universe (either by using lasers to determine his distance from the boundaries or may be using some ropes),
Even of there were a boundary of matter in a flat universe, velocity and position would still be relative so this is a false conclusion as well.
Now suppose the universe is infinite, now a person cannot determine his position in the universe.
You can not experimentally distinguish an infinite universe and a finite universe. If it were infinite then it could be very huge and have parts that look finite but are either just localized or else just repeat a larger number of times (so that it looks like you approach an edge or wander around back to the apparently same place).
And a finite universe could simply be much huger than any region you've looked at and so match what you see.
So whatever finite amount of observations you make there is an infinite universe and a finite universe that agree with what you've seen. Since this holds for any possible observations, it isn't even science to argue about finite versus infinite.
If you have a reason to think it is finite and a certain size, that is experimentally falsifiable. So that is fine.