Is gum pain normal after a temporary crown placed?

Not uncommon. The edges of crowns are often placed below the gum line. Trauma from the procedure will cause irritation of the gum tissues. Ideally, do not put anything on the tissue to soothe it. An anti inflammatory medication should help. If it persists more than 2-3 days, contact the dentist.
Yes. Probably from the procedure. Your dentist needed to put some cotton string between your tooth and gum to get a good impression. This bruises the gums. The pain will subside in a few days.
Yes. Gums do get inflammed little bit and soreness is possible.