Everything you mentioned happened to me when I first started doing applique on the machine. I found different types of thread needed different tensions, so play around with that on some scraps. Some threads are will break faster-you have to have the right needles with the right thread, plus on some of my rayons I will put a netting around the thread to keep in from coming off the spool too fast.
I also found that putting a lightweight stabilizer on the back of the block really helped. Or even some batting. You can then cut away what isn't sewn down when you are done.
Oh, also on the fusible, I found that using the lightest weight possible did better than the heavier ones. Hope this helps.