Yep. You say that like it's a bug or something, but it was always intended. You're given a summon spell for a reason.
Not necessarily. I genuinely don't know. There's this belief that when dismissed Orpheus will completely disappear from the game and is effectively disabled (like Karna). At least that's what some old comments on the GTS discord say.
But if the intention is that he can just be resummoned, then great. I have had some issues with that before but I think that was due to having a follower home mod set for him (which also caused havoc in his first quest as he would start walking home from solitudes gates).