I really can't help about needle. I've read mixed things about changing the needle bar or filing a 15x1 needle to make work in this machine. I will tell of an experience I had. I was cleaning and oiling a Franklin machine for a coworker (had belonged to his grandmother). Everything I read was that it took a 20x1. However, while cleaning I kept finding bits of broken needles. I decided I would very carefully try a 15x1. It worked perfectly without any adjustments or problems. It might not hurt to try. Did it have the short needle in it when you got it?
As far as the bobbin winding, my guess would be that something isn't lined up right. In some of the manuals I've read it suggests bending the guide. I know how fragile some of the metal pieces can be and that wouldn't be my first choice of options. Some of the other manuals show that there is an adjusting screw to change the position slightly to even out the bobbin winding. It appears on pages 46 & 56 of
this manual that the bobbin winder tension discs are on the left side of the thread guide piece. Does it screw apart? I'm wondering if there might be some way to adjust the bobbin winder itself to the right a bit. Or adjust the thread guide to the left a bit. I like the Singer 15s as you can unscrew and move the position of the tension guides to even out the bobbin winding.
Janey - Neat people never make the exciting discoveries I do.