Phone number or other contact info. Supposing you’re on good terms, they’re not someone you’re interested in romantically or the like (so none of the anxiety from that at least), what’s kept you from asking?
Supposing that something has on occasion, anyway.
I don’t think so, in a world where strangers add you all the time, possibly to harass you, a familiar face adding you is a very welcomed occurrence, as far as I know. Personally I never got any “rejection” on that front, but I’m sure it may change wildly from one demographic to the next.