I agree - the bobbin thread is causing that. If you hold onto your thread tails when you start sewing, it should take care of those nests.
As for the evenness of the stitches, I think I see what you mean - they aren't really straight. This is usually caused by a thread/fabric mismatch. It looks like you are using a fairly light, loosely-woven fabric. To get really straight stitches, you would need either a thinner thread, or a heavier fabric. If you were stitching on a single layer of fabric, then having two layers would probably help.