Regarding the stitch length lever moving.
If you take off the handwheel, you are able to access a screw with a screwdriver. The screw is also a shaft for the movement of the stitch length lever and it got some spring washer below the screw head. You may be able to fasten this screw more, and get higher friction to the stitch length lever, so it will not move that easy. But you can only do that to some level of friction.
If you need to have the mechanics explained, then this video do it quite well:
https://youtu.be/tRmQilh_UgI
I have fasten this screw as much as I can on my Singer 201k, and I still got the problem you describe. When I sew with a max stitch length of 4 mm on thick heavy fabric, then the lever moves and the stitch length may become 3.5 mm. At the moment I solved the problem by a elastic cord around the pillar of the machine, that is able to hold the lever down. You may put some thread around the screw head or something else to increase the friction. I should like to know, if you find a solution.