Sure, some things are impossible.
Dividing by zero is one case. However we do it all the time. Some clever bunnies discovered limits, and from that it followed that although a function might be discontinuous at zero, you could kinda just ignore that in the right circumstances and differential calculus was born.
A long time ago, people thought that if you went faster than 60 miles per hour you would die because you would not be able to breathe. Well, vehicles were made that went faster than that and nobody died -- well, not because they couldn't breathe...
So there seemed to be no limit. Newton's laws don't impose one.
Then some spoilsport came up with relativity and it shows that as you approach a particular speed your mass changes and the equation ends up dividing by zero at c.
No problem you might think -- if calculus can do it,, then so can a rocket! Unfortunately the math won't let you do it there. But the equation doesn't say you can't go faster than light, only that you can't ever (if you have mass) actually get to c. So maybe there's some trick to get past the barrier without going through it?
OK, but I bet if we ever do it, it's not going to be with any technology that we're familiar with today.
Now, perpetual motion. Read up on thermodynamics. It's intuitively correct. Maybe it's like Newton's laws. Maybe there is a bigger picture. Maybe that bigger picture allows some escape from it at very high or low temperatures, or at very small scale (think quantum mechanics), or under an intense gravitational field (think black holes), or something else.
If you find an "out" for this, then conceivably there is some way to have perpetual motion. As I said, it would pay to determine theoretically first where those holes are before you try to break them. Perhaps there is nothing with zero resistance, but -ve resistance is possible. But again, I suggest that if you do, you will be using stuff we've probably never seen before.
Maybe you find some external source (for another dimension or something) of power and can tap it. Again, I suspect that it will be theoretical physicists who will come up with this, not some guy in his garage spinning magnets, but stranger things have happened.
All anything that "breaks" the laws of physics needs is a demonstration. Once you have one the laws need amendment.
Imagine I came up with a nuclear reactor in 1750. It might be seen as a perpetual motion machine. But it's not, and physics shows what it actually is (tapping some energy from supernovae that was stored in elements heavier than iron).
Do I personally believe that we're ever going to see perpetual motion? No. If we saw something that appeared to be it, I would lay odds on it being something else -- and *that* would be a whole lot more interesting.