Tried flipping through the ROM to figure this out, but still having a hard time navigating the thing and the supplements, so probably just missed what the heck these things are and do...

First picture is LH side vacuum line that has a plastic do-hickie that seems to only let air to one way. The white cream side is labeled with DIST and the other side is CARB. What does this do and is it even on correctly?

The last pics are what I thought was some black pen lid that got jammed on something to plug it up, but when I looked closer it seems like it's some type of breather valve or some sensor related thing.

 

The blue/white valve is almost certainly part of the complex vacuum advance control system. Without some digging I can't offer more than that at the moment

The S58 manual will probably show it clearly. The S58 download is in one of the "How To" sticky threads at the top of this section

The blue valve thing looks like the dump valve for the cruise control. I don't know the exact function of that black cap, specifically, but I think it's a filter

Cheers
DD

 

This blue valve is part of the cruise control system that was added as a part of a TSB I believe. The cruise control solenoid wasn't releasing cruise quick enough and was hanging up so they added this valve to release the vacuum instantly. Mine looks identical to yours with the black cap and all.

 

Since the blue solenoid valve appears to be at the right front of the engine, it is the added dump valve for the cruise control. The black cap is indeed a filter. The exact same type of valve is also used as part of emissions control, and is mounted under the rear of the right side intake manifold where you really can't see it.