Asking for a letter of recommendation from professor that offered me a position
To your first question, yes.  There's nothing inherently rude about wanting to look for positions elsewhere despite having an offer.  Professors often want to their top students to stay on for graduate work, but these students often go to other, often better, schools (or don't pursue graduate studies) so your situation is completely normal.  Most professors wouldn't be offended by such information.  (There may be some cultures where professors' expectations are different, but not the ones I know about.)

I would suggest a frank discussion where you say that, while you'd be happy to continue your studies under that professor, there are some other schools in other countries you're interested in.  There's no need to tell him now, but if it comes up again, there's no need to withhold it either.  You can also bring it up as a question to see if he has any advice: "Yes, I'll probably apply to the program here, but I'm also thinking about trying to study at XXX--what do you think about that?"