So I've had Betta fish before, in the sense that most people have (small, round, *maybe* 1 gallon tanks without heater/filter). And just yesterday a friend of mine bought a Betta for me because I admired hers so much.
Well I bought a Vase (filled to the brim it's probably 1 gallon) a live plant, and Betta pellets. Then decided I wanted to put some rocks of mine in the tank, and googled how to boil rocks for a fishtank. Well it brought me here, and I did a ton and a half of reading last night (was not happy with having to wake up this morning I stayed up so late!) and registered as a user here
So I decided to used the vase as, well, probably a vase. We have an older tank that we've seemingly had forever. I put the measurements online and its a 5.5 gallon tank. I think he'll be happy with that!
So now come the questions:
1) My poor Betta is still in his cup because I didn't want to stress him out by moving him to the vase, then moving him into the other tank when I got it set up. How long will he be ok in there? It's been a day, do I need to change the water? He's very lively and has a voracious appetite! The reason I ask this is because,
2) I bought a 1-3 gallon pump/filter for my tank

I had a blonde moment and was thinking I needed to get the smallest size (I also had to pee like a wild raced horse, so this may have clouded my judgement a bit!). I figured I'd just take it in tomorrow and grab a 5 gallon pump/filter, no biggie, right?
But then....
3) Back when I bought the tank, probably 3+ years ago (may have had it longer) I bought a heater. I dont know what size tank it is for, but am assuming it can handle a 5 gallon tank. But it IS probably somewhere between 2-3 years old. And has been in our garage for probably 6 months. Is it ok to use? It seems to be in good shape. But at the bottom half inch or so, instead of being black, it has turned white (the stuff inside, not the glass). I have no idea what I'm doing, but was tempted to put it in to start heating the water so that he could have a warm home tonight....
4) I also bought a new light for the hood of the aquarium for the plant. It's an Aquarium Plant Growth Bulb, and is Pre-Tested 15W/120V Incandescent. It fits nicely into my hood, and is the same size visually as the previous bulb, but there is a warning on my hood that says only to use:
"tested tubular lamp 'rated 25 watts maximum'"
So how do I know if this light will be ok? Will it do something weird to the hood/explode if I use it?
So now I'm wondering if I shouldn't just leave him in the cup another day, get the new filter/pump (any brand will do? I bought a Tetra Whisper Internal Filter, will that work? Of course I need a bigger size

) and maybe find a new heater if it is deemed bad?
Forgot to add I bought a water conditioner, 'Tetra Betta Safe'. Will this work fine? I'm assuming it will but I thought I read something about it not removing 'something' (sorry, read it earlier today and have forgotten it, and have no idea where I saw it!) and that I had to have a filter that removed that 'something' or my fish would get sick...
So, to leave in cup, or not to leave in cup....that is the question!