1) Yes, always, Introducing a sick fish into your normal population can be devastating, and it's easily preventable with patience!
2) 20 long, less water, easier to change rapidly when medicating
3) Java fern, cheap submersible filter and a sponge filter (Overkill, but meh, the parasite meds can do a number on bacteria colonies), sand, floating plants for security. The tank is also low to the ground and mostly out of sight for extra security. Heater also, great for common bugs like ich
4) Depends where it comes from, usually my quarantine tank works as a growout too. I make sure whoever I've got in there is eating regularly on their own before I introduce them to the main tank, but usually they stay in there at least a month, usually they stay in there longer
5) I generally just use parasite guard for WC fish. For anything else, unless I'm treating a specific illness I just observe them and abstain from prophylactic treatment
6) Get em home, acclimate, observe for over a month

WC, acclimate, wait 24 hours or so, then treat with parasite guard for a round ( or two if a poly and they're exhibiting some kind of symptom). If after 30 days (this is a minimum!) they aren't exhibiting any sort of symptom and are eating well they've got a chance to graduate to the big boy tank
7) Just keep the tank clean and stable. Unless there's some kind of indication that there's something wrong, leave it alone imo