To answer your questions in order:
- In general, there's no formal way to prove that two programs do the same thing, and that has been proven. The next best thing is to device as many test cases as feasible and cross your fingers.
- If it doesn't exist, it is not a trivial exercise since you have to write a parser for XBasic and add semantic actions to generate equivalent Perl code from the parse tree. It can be done though.
It's too long ago I looked at BASIC to answer your third question.
Hope this helps, -gjb-