The nests on the bobbin side usually mean that there's not enough tension - either the presser foot is not down or the presser foot *is* down and the thread is by-passing the tension disks or the tension isn't set high enough. Usually, the tension will be slightly less than for machine guided sewing with the same materials and thread - not hugely so.
Set your bobbin tension to accommodate the thread you're using in the bobbin, then balance the upper tension with the bobbin tension so that you're getting a nice even stitch on the top side and the bobbin side of your fabric.
The fact that the thread is breaking could mean that the eye of the needle is too small for the thread or maybe there's a burr in the needle eye or in the hole in the needle plate that's only coming into play when you're moving the fabric freely under the presser foot.
Try changing your needle - put in either a larger needle or the same size needle with a large eye (metallic or topstitching)
Check the top and underside of the needle plate and the inside of the needle hole for nicks or tiny burrs that might be shredding your thread.
Sew slowly and make bigger stitches and see if the problem gets better or if it gets worse.
Post back and tell us what you find. :) Good luck!