Your "what is that?" is a vacuum solenoid. The vacuum lines appear to be correct. Do you not have the emission hose routing diagram in the fan shroud or core support? It might also be on the air cleaner. If not, you can find it in a tune up manual such as Chilton or Motor.
Have you checked to make sure the vacuum advance is working and not leaking? Are the centrifugal advance weights working? Is the timing properly set? How about the brake booster? Does it leak vacuum?
Try setting your timing to about 12 degrees initial at 750 RPM with the vacuum advance disconnected and plugged. You should have about 32-36 degrees total advance by 3000 RPM with the vacuum advance disconnected. Try disconnecting the line to the EGR valve and plugging it.
It sounds like the float level MAY be too high, and possibly the secondary air door may be opening too early.
In your THIRD picture, from the passenger side, there is an adjustment for the secondary air door. just above the words "to intake", there is a small screw facing out. Under it there is a small socket head set screw (takes an "Allen" wrench). Back off the set screw, back off the screw on the side counterclockwise until the secondary air door JUST opens, then turn the screw on the side clockwise until the air door JUST closes, then turn the screw no LESS than 3/4 turn further clockwise, and no MORE than 7/8 turn. HOLD the screw, and tighten the set screw.
Start the engine with the air cleaner off. The little gold link that runs from the choke pulloff (vacuum canister on the steel bracket on the passenger side front of the carb) should be almost at the FRONT of the slot in the tab on the side of the secondary air screw at idle. there should be LESS than 0.060" (1/16") clearance. If there is more, bend the link. I prefer 0.030" myself.
The float level you can't adjust without pulling the airhorn off the top. If you get REAL nervy, you can adjust it to 5/16". But you need manual to illustrate it. I set ALL Q-Jet floats to 5/16", after some 700-1000 of them I've never had a float level problem setting them at 5/16".
One other possibility is that the charcoal canister has gas in it, or is getting gas in it. Disconnect and plug the line to the charcoal canister, and try it.
Make sure the PCV valve is working properly. If you can pinch the vacuum hose to the PCV and change the idle speed noticeably, the valve is bad.
The idle mixture screws in the front on either side of the fuel inlet should be at around 3 1/2 turns. If you have to go more than a turn away from 3 1/2 in either direction on a stock engine, you have a problem.
If you intend to keep this thing and maintain it, I suggest you buy a copy of "Rochester Quadrajet" by Doug Roe. The reason is about 99% of people, "mechanics" included know nothing about a Q-Jet. That book is near gospel, and will rarely if ever steer you truly wrong.
Otherwise, drive the thing down to see Culero. He can fix it, if it can be fixed.
Oh, and now you know what I was doing instead of listening to idiot teachers in class ranting about politics.
(In all honesty we didn't have that problem here when I was in school)
