If the thread is shredding and breaking, there is an incompatibility of your needle, thread, and fabric. Could be old, bargain bin, or poor quality thread--does the thread have little "hairs" of thread lint sticking out of it--that's probably not good quality. Look for fresh, good quality thread. Try a brand new needle--a sharp if you are sewing woven fabric. Make sure the thread is not too big for the needle eye. Sometimes, a top-stitch needle or embroidery needle will work well on FMQ. (A top-stitch needle has a longer scarf which helps protect the thread during the multiple times the needle penetrates the fabric before the thread forms a stitch. Shredding means the thread is getting worn out before it forms a stitch. A piece of thread penetrates the fabric 10-20 times before it forms a stitch.) Could also be a snag somewhere that is damaging the thread.
Sewing Needle Troubleshooting Guide
SCHMETZ Household Needle Chart
Most FMQ instructions say the upper and bobbin tension should be the same, however, I find my machine works a bit better when the bobbin thread is just a little tighter than the upper thread. Then the bobbin thread does not "pop" up on the top of my fabric quite as much. It's probably something you will just need to experiment with in getting used to your machine.
P.S.--when threading your machine, make sure the Presser Foot is ALWAYS RAISED so the top thread will seat properly in the tension disk. Failure to do this will cause thread barfs (usually referred to as thread nests or bird nests) under your fabric. Also, before beginning your FMQ, ALWAYS PULL the bobbin thread to the top of the fabric, then hold both thread tails gently in your left hand while you slowly take the first couple of stitches.
How and Why to Bring up the Bobbin Thread