I'm new to quilting but have done some sewing (I realize they are different

) and I need some help. I started the Snowman Collector quilt 10 years ago and just got it back out. I have borders around each block. There is a little bit of fullness in the centers. I'm trying the sizing and letting it dry, but my question is can't I use my machine and when I quilt won't it take up some of the fullness?
Also, this pattern calls for 2 inch squares to create some borders. I'm percise in sewing them together and squaring them up. But when I sew them on to block, they get a little wavy. I've ironed them and taken them off, but when I put it back...... it happens again! Any suggestions?
Am I being too anal? There is applique on the blocks and lots of different pieces - should my quilt top be perfectly flat or is it okay to have a little puff here and there? I don't want to ruin this.
Thank you in advance for your help.
Carla