I'm new as well, so definitely don't take my word alone. I can't answer about the size, I think that would really depend on what sorts of fish you've got going in there. If you live in the US, Petco just started their 1$/gallon sale, my QT is a 10 gallon, if you've got a bigger display tank, you'll probably want a bigger QT since fish that need more room in the display tend to need more room in QT as well. What size is the tank that your fish will be going into/what fish are you planning to stock, always go bigger from the start if you can. Learned that the hard way.
As far as a bio wheel filter, it's my understanding that you should be running a QT as bare as possible. Should you need to treat your fish with chemicals, they usually say to remove all carbon, and sand, anything that holds stuff really and I'm pretty sure filter media is included in that if it's anything more than a bit of filter floss to polish the water (check out PolyFill, wal-mart or craft stores have it cheap for pillow making). Then if your fish were to have something then you may have issues with that bio wheel filter. Everyone I have spoken with has reccomended an AquaClear HOB, I have one and an Aqueon HOB, the Aqueon is a lot better at self priming but the AquaClear has more versatility. Of course if you're asking about the bio wheel filter because it's what you already have, then wait around for someone else to give you more info on the wheel itself since it can hold bad as well as good. But if it works without the wheel it would likely still be good for water circulation.
Personally I don't even use the light on my QT, right now it's sitting right next to my DT in a bright room so it just gets some residual light. I'll be getting my fish used to my light cycle closer to when it's time to put them in the tank.
Heater is needed so you're right there, from what I understand it's easiest if you keep it the same temperature as your regular tank for ease when it's time to transfer the fish over.
From my research, again this is a big area where I'm new, but I can share what I've read so far. Anyway from what I've read so far, simply observing a fish isn't going to catch some things. Many LFS run low levels of copper in their system, this keeps the fish from outwardly displaying symptoms even if they might still have something. That and some things just are more visual than others. I tend to er on the side of caution, so I think I'm going to be treating my fish in QT but I have yet to come to any conclusions on that but to me knowing that there are some pests and diseases that aren't displayed visually is enough to make me want to treat proactively.
