You have the right bobbin, these machines take an odd size bobbin and I don't think any other (at least common) would even slighly fit this machine. The question might be bobbin case, I have to look it up, but early Featherweights differ somewhat from the later ones regarding a few aspects, but generally they all are of the same build.
Clean and oil best you can, particularly the bobbin area. There are several user manuals as well as
service manuals available on the web. Unscrew needle plate, take of face plate, etc. cleand and oil every where.
Check that the needle is in the corret way, (flat side to the left and it threads from right to left).
Check top tension mechanism, when threaded the two disks should grip the thread firmly when presser bar lever is dow, when up it should release. It should gradually increase tension from 0 (very loose) to 9 (very tight). Test sew with two layers of light cotton (shirt / quilting weight) and sew-it-all type thread. Assume tension is correct some where between 4 and 5 and take it from there.
This lady's blog is very good and she seem to know the Featherweight well. You have a very nice machine there :- )