checked baggage: answers, yes, yes, yes, and yes. you can pack it all. don't know how much you are carrying, but I would carry labeled items so if they search your baggage they won't think it's something bad.
honestly I have carried my e-cig and refills on the plane, so put them in the carryon totes they look through. the rest I put in my checked bag, but I wasn't carrying huge amounts. one small bottle of e-liguid and other necessities all bundled up nice.