Can you post a picture of the cover? There are people here who can tell you exactly what you need to know.
The holes that I remember for attaching things are just to the right of the needle plate on the bed of the actual machine. You might be looking at an oil hole.
Singer used a lot of odd thread sizes. I doubt the big box stores would have the right screw. You might be able to find the right screw at Sew-Classic.com
Rodney