The Nikon F3 uses a relay mirror for the photocell of the light meter (attached to the rear of the reflex mirror holder). See page M11 and M13 in the F3 repair manual in the following link.
[F3 owners might want to save a copy of this file for further reference.]
http://ss-it.de/data/servicemanuals/F3 (V. 1).pdf
I suspect that the relay mirror intermittently intrudes into the light path between the bottom of the scene and the area along the top of the film gate casting its shadow upon the film. If so, this would show along the bottom edge of the developed film frame. That’s what we see in the some of the photos displayed by the originator of this thread. (The repair manual refers to it as the "metering mirror.")
This could happen if the mirror sometimes rebounds upon striking the stop pad surrounding the viewing screen mount, possibly sticking in this position as the shutter cycles. It could also happen if the mirror occasionally fails to fully come to rest against the pad. That this happens intermittently suggests sticking due to dried or oxidized lubricant.
Some of the frames I viewed also seemed to exhibit differential exposure across the long dimension of the frame. That would not be related to the relay mirror. This seems to be the case in the two photos shown in post #4. That might also be the case with negative frames #22, 23. If so, this problem is likely related to the uneven travel of one of the shutter curtains. This too can be intermittent.
The film transport problem is a separate issue. As others have commented, this camera needs the attention of a qualified technician experienced in the servicing of the Nikon F3 camera.