Hi A.,
I usually try to have them going potty quite a bit before I start putting underwear on them...that way they actually know what they are trying to do before you expect them to be big girls or big boys. I'm pretty sure at 2 1/2 she is ready...she just isn't quite understanding it all yet. Pull-ups are okay, but just using diapers are fine. Yes, it is not unusual for her to still be pooping in her diaper...that is sometimes the hardest part of potty training...sometimes they do this at around the same time everyday, so if you can sit her on the potty about that time it might help.
I know you don't like to bribe her to go potty, but it works, and if it makes it easier for her and you, why not?! At my house, when they actually go potty they get a treat, like a smartie or an m&m, but only if they do their job. Think of it as a reward for a job well done. There is nothing wrong with positive responses to good things. I've noticed that sometimes we are right on top of getting after our children for doing something wrong, but when they do something good we forget to reward them for that, and we need to give them positive input as well. You have to be consistent with everything. Don't give in...make your rules and keep them. If you don't, children don't learn anything, and sometimes get confused, but usually they are so smart they know you will give in, so of course they keep trying to do it the easy way, and still get the reward.
Don't give up, she will surprise you one of these days and it will be like she has been doing it forever. Also, don't be surprised if after she seems to have it all figured out she has a set-back once in awhile. Just stick with your rules, and it won't last long.
Good Luck!
C.