A good piercer would have to look at it and tell you if it would be a good idea or not. Is it the center lip? If it's a side lip, it would be easy to put it in an ever so slightly different spot, but if it's the center lip, that would be more difficult. However, it is has healed super-well, it should be okay.
When you pinch it and wiggle your fingers around, can you feel a blob of scar tissue inside there, or no? I pierced my hand webbing once and that happened (and it even kind of hurts a little, too, when I pinch it), so if it's a case like that, I'd say don't get it pierced again, but if it seems super-well healed and a piercer says it's okay, then go for it!
I don't know how your stud can just fall out unless you're wearing a fishtail labret. It depends on how long the jewelry has been out for. If it was recent, they can just put in new sterilized jewelry. If it has started to heal, they'll have to repierce it. You may or may not have to pay for that.
No way to tell. Its pretty common for lip piercings to only heal up halfway. Meaning that they look like they're open but you can stick anything through it. Massage it alot to encourage it healing
Your lip will heal with the hoop through it. In a couple years, when you remove the hoop you will have a hole in your lip.
Yes
5 days is pretty new so swelling is expected. Just keep taking good care of it and the swelling will go away. You can try letting ice melt in your mouth or a warm towel. Keep talking to a minimum and dont play with the piercing.
Move out.
Put water on it.
i think a few weeks but no offence but lip peircings are stupid
6~8 weeks
Follow your aftercare instructions.
Stop touching it so it can heal.
5 years or so.