Trouble with old sewing machine

[JEmmelkamp]

I think you are pretty close on the threading. In picture #5 stay behind the curved rod guide when you go between the tension disks the over it and then simply under the small spring (not around it). This is before you go through the tension lever that goes up & down. The small spring is there to keep the thread behind the curved rod when the tension lever goes downward.
The movement in the bobbin area is normal & OK…. There has to be enough room for the thread to pass around the bobbin case and up through the space between the shuttle driver race and the tail of the shuttle.
Do you have a loaded bobbin in the bobbin case? The bobbin looks like two small disks with a tube between them. It is wound with thread in the apparatus up near the hand wheel. The bobbin is small enough to sit inside the bobbin case, and the thread on the bobbin is passed under a flat spring on the flat side of the bobbin case. When you load the bobbin case in the machine, pull about 2 inches of thread out and let it hand loose on the right side of that little finger on the bobbin case.
In the pictures from your first post, #7 and #8 show the shuttle hook rotating to the left (back of the machine) and then coming toward the front and catching the thread loop. This is correct. If you put the machine in this position again, hold the end of the thread to the right of the needle, and watch as you turn the hand wheel. The shuttle hook will catch the loop pulling it to the right or forward, go half a turn and it should slip off the end on the hook. At this instant, the tension lever jerks the thread up and it will catch on the mounting shaft of the bobbin case. Normally it would slip over the bobbin case thereby completing one stitch ( a single loop around the bobbin thread).
Before you start sewing, and before you put material under the needle, hold the end of the thread to the right of the needle and turn the hand wheel around once. This will pass the thread around the bobbin once. When you then slide something thin under the foot, it will lift the bobbin thread up to the top side. Now hold both threads, put the material under the presser foot and let it down. The machine should now sew!