> But we have sent probes to other worlds? What is science fiction about this?
Probes aren't space travel for humans.
> A manned mission to Mars is entirely feasible with current technology.
As no manned missions to Mars have ever proven this conjecture, it is still entirely speculation on your part.
> A manned mission to another solar system is going to be very-very difficult, we'd need generational space ship/habitats. Note that difficult is not the same as impossible.
No, it is impossible. Humans cannot survive in space that long. Never have, currently can't, and there's no precedent to assume it ever becomes possible. Pure speculation on your part.