Hi A.,
I can completely understand your anxiety about flying alone with your son for the first time! I had to first fly alone with my daughter when she was one, to visit her dad who was away on a job for the summer. I found it a challenge to keep her occupied on the plane and was worried about how others might react. I found people to be very understanding for the most part and ended up sitting next to a nice grandpa who kept my daughter engaged with a magazine!
Since that time, we've flown together many times and this summer she will be 3 when we fly again. Since your son is 2 1/2 it will be a bit of a challenge, but he might surprise you. We did invest in a portable DVD player and pull it out when we've exhausted all the books and other toys we've brought. I don't give my daughter a ton of sweets, but I have played a game where I take mini M&Ms and put one in my hand, giving clues about the color. He may be a bit young for that, but if he knows some colors, you can have him guess. I once spent 15 minutes playing this game! And, she didn't end up eating a ton of candy in the long run. :)
We've never taken a car seat, actually, but it isn't a bad idea. It's interesting...some airlines will be more strict than others on that...I've also had some flight attendants who have been judgmental. Flying alone with a toddler is challenging in terms of everything you are carrying as well as the baby. I had a flight attendant lecture me mid-flight about not having a car seat in front of other passengers. While I see her point, I didn't think it was appropriate to do that in that time/place.
It'll be just fine, though, and once you get that first flying under your belt, you'll be a pro in no time!