1. I figure I could fit 3 plants in a normal walk in closet, but how much lighting would be needed?
a 250watt hps should do fine, but there will be a bit of effort and money envolved to get it all working properly...

2. How much does the average plant yield once it has been cut, dried, and what ever else I don't know yet that has to be done to it?
There are alot of different things that can affect yeild, probably the most important of which is the strain... so the bigger the yeilder, the bigger the yeild...

3. Am I an idiot for considering growing in an apartment. I'm sick of having to go through shitty dealers in order to get shitty weed though
no, of course not... growing instead of buying is always good...

4. Where can I get seeds from (this I havn't looked for yet.) I know they are easy to find on the internet, but is it really safe to order that way.
yeh, its safe from the right people, you can get seeds in weed sometimes, so if you can, those will do for a starter grow...

my advice would be instead of growing them in the cupboard from seed, to get quite a big closet, or something a little smaller than a walk in cupboard, then vegg. in that, with 3 plants 2 months ahead of the next 3 you will be able to have 6 plants in vegg. (3 medium size and 3 small,) and 3 plants in the walk in cupboard, with the lights on 12/12 for flowering, then, after 2 months (the average flowering time) harvest the buds, and put the big vegged plants in to flower, and plant 3 more seeds for the vegg room, that way you can harvest three plants every two months - which is niiice....

the reason i say to use the walk-in for flowering is because this is when your plants will be at their biggest, (and their smelliest) so like perp said, make sure to take care of the smell...

that should help you, if you can understand what i just said... lol, hopefully you can - good luck with your plans, it may take a while for you to harvest, but it will be well worth it -peace...

-just my two cents...