If I were to use my sewing machine on felted fabric, I would worry about the fuzz gumming up my machine. I think I would put some backing on the underside so the felt wouldn't come into contact with the feed dogs. You can get backings that dissolve in water.
I'm not sure that single-thread sewing will show up that much on a felted item, but you could certainly play with it. Look for lots of contrast in your choice of thread color.
I have seen some items that have a knitted bodice attached to a sewn skirt, but I would sew the two pieces together by hand.
I'm a very experienced sewer and felter, but these are only my opinions. I say go experiment and have fun.
Congrats on the new machine!!