I’d not worry about Valentines Day. It’s just a day. Don’t worry about kissing or other things.

If you like her and want to know her as a person then you do need to communicate and spend more time with her. It sounds like you two barely know each other at this point. Your conversations are short and infrequent and only met 5 times. I am not sure what type of moves you are talking about. Romantic? You don’t even know her much

Yes it’s ok to contact her again when she’s back from a trip. If she responds, set up a meeting if she’s up to it but no do not ask about Valentines Day. And no do not be persistent.

If the guy barely talked to me or saw me but then wants romantic dates or being persistent, I’d be creeped out.