I'm wondering if the needle is hitting the plate, thus bending and breaking needles. You should be able to see pitting around the hole if this is the case, and that could force the needle higher into the bar. I don't use the plate with the small hole in it for that reason, I use the one for zigzag and fancy stitches. The needle can hit the plate just trying to sew over patchwork seams, fancy trims, or if you tug on the fabric. Have done it several times.
The needle threader should have a very fine wire, which should go through the eye of the needle and pick up the thread. If the needle isn't inserted properly the threader won't work. Mine was 'off' last week and I only had to bend it a little till it lined up with the eye. I think you need someone to look at the machine.