Rear wheel won't stay in position
It's some combination of:

QR springs not pointing the right direction. Try removing them completely while working on this, which can also help with the next thing.
Relatively thin steel dropouts not playing nice with this combination of QR skewer and axle ends. If the axle ends are poking through the dropouts and touching the QR nut or cam, or doing so as the whole thing presses together, it won't clamp right. This can happen sometimes putting new hubs and QRs on old steel frames. Solve by using a more traditional kind of QR, i.e. a steel internal cam one, and measuring to corrobrate you are well away from this being able to happen. Taking away the springs completely can sometimes be the quick fix to this problem.
Cam surfaces on the QR need lubrication. Put a drop of oil on the barrel that the lever pivots around.
The QR has some worn parts not seen in the photo, like the plastic bushing part.
You're undertightening the QR. Lubrication can help with this, or not, since external cam QRs are basically bad.
If your dropout alignment is wrong, for example by way of putting a 130 or 135 wheel in a narrower rear end, the QR is now needing to flex the dropouts back into being parallel before clamping happens. This can cause or add to the problem.
You've got horizontal dropouts and the external cam QR isn't providing enough holding force.