In relic recon, once you get the +15 upgraded relics from the boxes, do you just have them forever even if not fast equipped? More importantly: Can I use this event to get relics for multiple characters?

I just pulled Hyacine, and I selected her for this event to get her a full set with her recommended main stat and a few substats. But because she's a support and I have other characters I want to focus on building more, I don't want to waste so many tickets trying to get the perfect relics for her. So, can I do that and get different relics for different characters after equipping them on her or can I only get 6 relics?

(Mostly irrelevant rambling)

Also, I chose characters with the relics that are least efficient for me to farm. If I had it my way, I'd have chosen her main relic set (warrior goddess) and Dan Heng's planar ornament set (Lushaka) because those are inefficient domains for me to farm, while Hyacine's planar set (giant tree) is in the same domain as Evernight's (bone collection) and DHPT's main set (recluse) is in the same domain as Evernight's (world-remaking deliverer) (Evernight is very efficient to farm. So even though I think she may have some of the most stringent stat requirements I don't want to select her for this event. I really don't want to farm warrior goddess. I have no use for Wavestrider Captain. Dan Heng should be fine with some other planar ornament set.