well if you're using your closet you don't need a tent. That's what I use is a closet. I have a veg box and closet for flower. If smell is going to be a prob, get a inline fan and a carbon filter. Plants stink.
Yes I forgot to mention to put an osilating fan in there if possible to do exactly as you said.
when to start your nutes really depends on the soil you have. I use Miricle Grow time released and I don't give ANY nutes for the first 2 months of veg, then flip them into 12/12 and give them a weak solution of Miricle Grow all purpose nutes for a week then the 2nd week I give them a weak solution of halve veg/flower nutes and then see how the plant reacats to it and then just bloom nutes from then on.
I'm not saying you should do this but it's what I do. I'm no expert or anything I only got 6-7 grows under my belt. Still learning lots, but know the basics.