#1 - That's a stock sway bar mount. Look for cracking.
#2 - That looks to be a turbo valve cover.
#3 - Pacific Oil Cooler does a great job with oil tank and engine cooler testing, reconditioning, and inspection:
https://www.oilcoolers.com/contact-us/
I sent my engine oil cooler to them for cleaning/inspection. I stripped the parts off my oil tank, took it to a local machine ship that hot-tanked it. I then repainted it with engine enamel.
#4 - Sorry - I'm not sure about the oil cooler. I thought '77 had the trombone cooler.
#5 - The black is road grime. Some Simple Green and a stiff brush should remove it.
#6 - Those look to be Porsche pre-75 exhaust. SSI's are full stainless steel and look just like those only shiny. It's possible those are very dirty. If a magnet readily sticks then they're just factory steel and not stainless SSI's.
I have a '75 Targa that I rebuilt and still have. Some things I recommend/learned along the way:
Rebuilding a 2.7 isn't cheap. I rebuilt mine. Somebody suggested at the start of my project to consider finding a used 3.0 and rebuilding it if needed. There were days that I wished I had listened. If I had to rebuild today I think I would go that route.
Unless you're attached to CIS, it may be time to look at alternate induction. EFI kits are so much easier to piece together now than when I started my project. I fought a bit of CIS trouble.
And the "general stuff":
Pull the carpet and get into the tunnel while the engine/trans is out. Replace all the fuel lines. Look at moving the fuel pump forward if yours is installed in back. Definitely do the suspension while the engine is out. Pull the entire shift linkage/rod and completely rebuild that before putting the engine back in. Rebuild the pedal cluster and all the throttle linkages while you're in there. Look at PMB for brake caliper rebuild/exchange. Replace all the brake lines. Look at all the wiring and upgrade/fix while things are apart. Consider changing that long cable between the battery and the starter.
It's easier to take the whole car apart and put it together right than it is to tackle portions and drive it in-between mini-projects. If you're going to have the car painted then absolutely strip it to the shell and do it right.