My first response was, relax! she's talking away and doing great! But, after reading the other posts, I do agree with the moms that said, if you have any doubts talk to her pediatrician, it will give you peace of mind and the dr will be able to see how she responds to questions the dr asks.
It is very normal for someone your daughters age to say No to every question - even ones where it doesn't really fit what was asked, they seem to love the word.
To increase the amount you talk to her and to help her learn more sentence structure (although it seems hers is pretty good already), just babble on about whatever you are doing or observing and try to engage her in the process or follow her lead when she starts talking about something. If she says "pretty horse" as you drive by one, you can just babble on not waiting for any answers "did you see the pretty horse? he's standing in the field. look how fast he can run! " Do this when you are cooking, or any other task you are doing. It doesn't matter how silly you feel, it won't seem silly to your daughter.
I would keep trying to make friends with the moms in the playgroup, yes they are going to brag about how great their children are, you can either take the opportunity to do the same about yours, or quietly let them finish and then ask if they've read any good books - either for themselves or to their little ones. With every kid there will be things the other child can do better than yours and things your child does that shine above theirs.
People brag about their kids because it's an easy way to talk to strangers, and because we moms really are proud of our little ones. If you can let the other moms get that out of their system and then ask them a simple question about themselves, maybe they'll move on to their next favorite topic and you'll find something to identify with. Eventually, you are going to really need for your daughter to have a playdate (maybe not for a year of 2), but when you do, you'll be far more comfortable if you are on friendly terms with the parents. I am very shy as well. I really believe that is how the "firm handshake introduction" for business settings developed, it's a ritual, an expected way to begin a conversation, introduce yourself and get down to business, it doesn't matter if you are shy or not because this is how you do it. Unfortunately, there is no real ritual for introducing oneself on the playground, but if you develop a strategy for yourself beforehand, you may eventually find a way around your shyness.