daisywreath,
Welcome to the Quilting Board Forum.
This is the vintage machine section, you can post the questions here or on the other section.
First you really need to get some Tri-Flow oil. I used to say "oil is oil is oil" but since working with sewing machines and using the Tri-Flow and regular sewing machine oil side by side and seeing just how much better the Tri-Flow is, that's all I use now.
Feed dogs / pressure foot problem:
First raise the machine up on it's hinges like you did in your second picture. Push the feed dog buttons up and down and watch what moves. Oil all of it thoroughly. On the left side is the plunger that moves in and out of the feed dog mechanism, that must be free to move completely back and forth. That little plunger is tapered on the left side and that is what controls the position of the feed dogs. Tri-Flow them thoroughly.
After lubing them move them up and down and up and down and up and down until they are free.
Next, turn the hand wheel until the feed dogs are lowered below the needle plate. Then lower the presser foot. If there is any clearance between the foot and the needle plate the fabric will slip as the feed dogs drop during their movement cycle.
If there is any clearance then the pressure foot shaft should be adjusted.
Stitch regulator knob:
Remove the top of the machine. Look down inside as you turn the knob through it's movement right to left. That is a very complicated mechanism. It's connected to the ZZ and pattern controls. Everything must be free to move. So, if it moves, OIL IT, OIL IT, OIL IT. And as you oil it, keep turning it through its right to left movement and watching to see what moves.
Heat won't hurt it either, but Tri-Flow will work wonders in that machine.
Joe