Your first question should be: Is the word 'perchance' used nowadays? And the answer is: No - not unless you are performing a Shakespeare play. The word is archaic rather than simply 'outdated'. It has not been in current use for many hundreds of years.

No Pavel this is a word from Shakespeare's time and is not really used today,unless you want to quote from Shakespeare's plays,for example the most famous one would be "To sleep,perchance to dream" from the play Hamlet.

Yes, Well at lest in the area I live. It's usually used to emphases the 'likelihood' of something. Do you have any more in stock? Do you perchance have any more in stock?

I'd actually say that "perchance" is outdated, on the verge of being archaic, but I think there are people who use it, at least in literary work (beyond Shakespeare).