Welcome to our forum.
As for the "T" handle on the drain, it should NOT come out and if you were able to put it back in, please let your dealer know about the experience. IMO the slice valve needs to be replaced, as it will come out again in the future, but I would certainly recommend a fair weather day. We have 21° weather today and it is not the kind of weather that I would want to drain the spa for a "glue" repair. Monitor it carefully for any dripping and let your dealer know and so note your records.The drain is a direct connection to the "suction" side of the plumbing system and does call for some minor "plumbing surgery" for it to be cut out and replaced. The "T" handle raises and lowers a "paddle" or "gate" to allow the water to drain. If it pulled out, and it shouldn't, it could have gone back into it's socket, but rest assured it will come out again.