Hi pino,
Congrats on ur new keet

In case you didn't know...you really should have quarantined the new one for at least 30-45 days before putting him next to Pino. I don't know if it's too late to do so, but you might want to do it anyway for safety's sake.
As for the diarrhea...it's pretty common with new arrivals. Being in a new environment and being scared and stressed can cause diarrhea. So calm down and don't worry too much about it quite yet. Just keep an eye on it and if it doesn't straighten out soon, then take her to Avian vet. It's actually a good idea to get a checkup anyway

It's also pretty normal that you haven't seen the new kid eat or drink yet. They are too scared to eat/drink in front of you. It's a good sign that you've seen her perched on food dish tho! Check dish for empty seed hulls..if there are hulls she has been eating.
Clipped wings will grow back with the next molt.Any idea how old she is? Does she still have baby stripes on her forehead leading down to her cere?
The band on her leg is breeder info. DON'T try to remove it yourself. If you want it removed have a vet or someone with experience do it. I've never had a bird with a band, but from what I've heard it's pretty hard to remove and you could injure your bird trying to remove it.
Personally I think I would want it off. Only because I think it would be annoying to a bird to have a band. Maybe it really doesn't bother them at all? I just know it would bug ME if i were a bird! LOL