OK! I got some ideas on the first one as I know it a bit!
I think I see a black tube running as marked in red and that is where the engine running makes a vacuum on that tube. I might think the tube has a central point where it may connect together with some other tubes on a fitting of some type.
Maybe something that looks like a plastic "tree" with different tubes on each limb of the tree. Maybe a "manifold" if that is a thing you know about?
What I think is when the engine runs it makes a vacuum and this tube may connect to the heater controls that are then connected to the vacuum.
Testing can be kind of simple if we have the engine running and get the tube off this valve thing, we can put a finger over the tube end and feel it suck on our finger if there is vacuum there! Knowing where that vacuum comes from so we can set the control that cuts the vacuum on and off may be a guess that takes some looking??/
But the idea is the vacuum pulls on the inside of this valve and makes the lever on the side move up and down. that moving moves the flap inside that changes where the air moves. Maybe flops from one position to the other to change from inside air recirculating to outside air or from floor heat to defroster?
Click this picture to get a better view!
But I think that will have a spring to keep it one direction until there is vacuum puts on to move it. So if you grab that part sticking out the top, it probably moves up and down even without taking the vacuum line off.
If you have a helper to change the hear and air settings inside, you might see this thing move. Or if you have the heat or air inside running and somebody to tell you what it changes, you might grab it and open and close it and let them tell you what the air does inside.
Like moving the damper on a wood stove pipe, if that's one you've been around?
One of the bad things about these rubber vacuum lines is that they get brittle and have leaks that are hard to find. Sometimes it is easy to spot because the fall apart when you touch them but other times it is a slit along a bottom side where it's a trick to find them!
When they get brittle, some just go through and change all they can see!
But that brings up a question of what they call things! I think of engine driven as things like the blade on a lawn mower. But they might call it engine driven if it had to have the engine running to make the vacuum to move them??
Some place there has to be a hundred people dreaming up ways to confuse us!!