Is this sentence grammatically correct?

It's grammatically correct, but if you wish to be a writer you should bear in mind something Samuel Clemens (Mark Twain) said. "The difference between the right word and the almost right word is the difference between lightning and a lightning bug."  Unless your intention is to deliberately hurt the other person, you should not use the phrase "give up here." It's denigrating. It would be better to say "to stop here" or "to pause here.".....even better would be "to consider stopping here." You're implying the person is a quitter or lacks the will to try. It's similar to implying he or she is a loser.

Not quite. "Would you like to continue learning Spanish with me, or would you like to give up now?"

Would you like to continue to learn Spanish with me or would you like to give up here?
OR
Do you want to continue to learn Spanish with me or give up?