I think it is the invisible threads and the metallic threads that are not recommended for use with small children. However, that could happen with any thread if a baby gets fingers caught in it, but seems to be more likely with those two types of thread. Whatever thread you use, make sure your thread tension is correct, so little fingers can't get caught.
Quilting density: 3" to 4" apart is fine.
Thread - a good polyester thread should wear well, as would cotton or cottonpolyester. If you are worried about the thread wearing out, use the thread you feel is stronger.