I think the small lever on the right side of transmission is to select draft control or position control. When you are using a ground engaging implement like a plow or disc you can use draft sensing. It senses when the implement starts to pull harder and raises the hitch arms to maintain a manageable load on the tractor. When it is set in position control, the hitch arms will stay in whatever position you place them, this works better for grader blades etc. Position control is with the lever up in a vertical position.
If your lift cylinders are acting strange it might have something to do with the draft sensing. If you do need parts, I would assume a New Holland dealer can get what you need.
I'm not sure on the PTO engagement, If that tractor doesn't have live PTO, you may need to push in the clutch pedal to engage the pto.
Hope some of this helps. Steveguy