First be sure that when you cut your fabric you are on the straight of grain. It does and will distort blocks if they are not.
For the binding, leave at least 3-4" all the way around the quilt while you are quilting, quilting takes up fabric.
Second, don't trim the quilt until after you have sewn on the binding to the front of the quilt. Then trim, this will prevent the backing from shrinking back, it will be caught in your 1/4" seams.
Pinning every 3-4" is important, but I always use a spray basting product as well, It does help.
While I'm quilting, I start in the center of the quilt, place my left hand underneath, and feel that it is smooth. If I feel any movement in the fabric, I will adjust it before continuing.
When I move to another area, I try to start as close to where I just left off. Say I finished on the right bottom corner of a block, I would go to the left bottom corner of the next block. If you go to the next block and leave a large gap of fabric unquilted, as you work your way back to the previous quilting, it will inevitably have a pucker because the machine is pushing the fabric against a fixed point. I hope this makes sense, it's easier to show than explain.
PM me anytime if I can help you, I've hand and machine quilted for over 40 years and probably made every mistake in the book at one time or another.