1. Other than, say, cameo clothing, a shotgun, a knife for dressing, what other equipment will I absolutely need? I speculate I may have to buy one of those bright orange vests so that other hunters may see me.
You need comfortable, durable clothing, with a way to carry your necessities: license/tags, ammo, knife, light. I hunted for years in my farmwork overalls and a plaid top coat. If you are going to be distant from water/food/shelter, then you may want a water bottle/canteen, energy bars, and a poncho/raingear.
Adding purpose made hunting clothing is nice, but expensive, and you are not as likely to where them in other situations. See what you have in outdoor wear/work clothes and add what you need. You have years to add fancier items.
Orange is a legal necessity for some, a safety must for others. I happen to be the latter. I wear orange for turkey. I'd rather go home empty handed than dead.
2. I'm thinking of buying a portable heater (that uses propane; I assume that even with proper clothing, it'll be nice to have a heater as I will be outside in colder weather). Yay or nay for bringing heaters while hunting?
I have seen them used in permanent blinds (be careful of CO poisoning), but not in the field. I have also seen the chemical heat generating bags. I have not used either.
3. How difficult is it to dress a deer?
I grew up in a slaughter house, so I am a little biased. Due to the smallish size and often lack of hoist to hold the carcass in the field, it can be more difficult than beef, but not the pain of scraping hogs. About like mutton. If you are squeamish, that is a different issue to which I cannot relate.
4. The average deer you guys have hunted - if counting only meals for one average-sized male adult, how much meat does each hunted animal yield (how many meals)?
Average 2.5 year olds yield about 75 pounds of boned out meat. Young animals considerablu less.