Hello Nika, Yes , in that case it is used as an interjection and means: "you are welcome"

It's up to you what you say, you can reply in many ways.

Yes, you can say "Anytime!" instead of "You're welcome!" or "No problem!"

When compressed into a single word, 'anytime' is usually an adverb. Like: "He's about to arrive anytime." In the sense of "You're welcome!" I would use "any time": "Hey, thanks mate!" "Sure, any time!" There aren't very strict rules for it, to be honest. Except when you say: "I won't have any time until Friday." Then it definitely needs to be two separate words!