Hi! Welcome to TE!
To answer your questions:
1. Yes, I wear a jersey every time I ride, or almost. If I'm commuting in winter, I might just throw a jacket over a wool baselayer if I'll be wearing the jacket on the way home too. (I live in AZ--we don't really have winter here!) A wicking t-shirt and cycling shorts is fine for short rides; what jerseys get you is pockets so you can stash your stuff. Keys, phone, snacks, and so forth.
2. There's no good way to answer that question, since each brand is cut and sized a bit differently. I look for bright colors and/or appealing designs, a cut that fits, no elastic at the hem (or just at the front), and 3 deep pockets (an extra zippered pocket is a bonus). Also, no cap sleeves and sleeves have to be long enough to play nicely with arm warmers. Bear in mind that most brands tend to run small.
3. Short-sleeve or long-sleeve (for winter). Never sleeveless. Kit...well, that depends. Not that I own any.
4. However many you want and will fit in your closet! (Though I suggest you actually use them all...)