Kind of hard to confirm, but since there are Helpers which seem to perform a lot better than they should, even assuming Affection, i'd think Equip is carried over by Helpers. About Ampy's: not the slightest clue whether they're counted in or not >.<
Also, yeah, totally agreed on the HP. Feeling that with Cepha myself - having low HP makes her feel way too squishy, regardless of DEF =/