Hi Welcome to the boards!
Hmm.. new needle bar assembly.
I found a photo of a Singer 301 longbed so you can sort of see how the basic set up is :
http://mysewingmachineobsession.blog...-long-bed.html
That piece that looks like it should connect might belong with the round part with the stem the piece your trying to connect. I think that's what makes the bar go up and down. Does it (the machine) have the ability to zig zag? If it does maybe setting it to a basic straight stitch could 'reset' parts to where they should go. It may help with connecting things.
this the bottom of the machine, where the bobbin is located at. Maybe this video could help?
https://www.youtube.com/watch?v=y0YGkYvhCFs
This one is repairing the hand wheel where there is a flat spot on the friction gear:
https://www.youtube.com/watch?v=vWR6BfXOfzY
http://mysewingmachineobsession.blog...with-elna.html
I'll keep digging around to see what turns up.