The green spots are mold, the reddish are rust. To attack the mold, use vinegar. Remove the part from the bike if possible. Soak a towel (paper or cloth) in vinegar and lay it on the green stuff. An hour should be plenty. Then rub it off using some "elbow grease". Flush with clean water then dry.

[Edit: don't use abrasives on plastic covers or parts]

For the rust, I've had much success using #0000 steel wool or aluminum foil scrunched in a wad and WD40 or motor oil. I've heard beer works on rust also, but never tried it. Take it slow and you'll be amazed at the results. Polish with a non-abrasive metal polish.

 

I've heard beer works on rust also

I have heard that drinking beer while doing this can help.

Seriously though, I've heard of using coke-a-cola. My brother likes to restore old tools, I know he's soaked things like metal clamps in coke and it seems to do the trick. Not a huge help but anything you can remove and soak this may work. Even things like the little air cover screws.

Regarding the aircover: I think I might have one that could match yours. It's from my 99 750 ACE. Is your 2001 ACE a 750? I assume it would be interchangeable but we'd want to make sure. I'll see if I can dig it out and try to get a decent pic for you. If it's a match and you want it, its yours for whatever the postage would be.

 

Sitting for 18 years. It looks like you cleaned it up some, and I will assume you checked out the electricals / mechanicals, but just in case:
Does the bike turn over / start / run? If so, do all the switches and lights work? Did the owner run the bike and change the oil on a regular basis while it sat? Was the coolant changed out in that time?

And I second the 0000 steel wool rather than a wire wheel. The chrome might end up looking good enough to not have to paint it. Good luck with it.

 

The wheels may be ok with the steel wool. Possibly just remove the chrome fork covers and get some of the old rubber accordian covers. if the tubes are rusted in the seal travel area, clean carefully and polish smooth to prevent seal damage, Not sure I've seen an Ace neglected that bad before.

like these but for the correct fork tube diameter https://ae01.alicdn.com/kf/HTB1EHK1...-Fork-Cover-Gaiters-Gators-Boot-Shock-Protector-Dust-Guard-for-Off-Road-Pit.jpg

 

Beware of plastic like the head light shell, the instrument cover on the tank, the air filter box and probably more I'm not thinking of, steel wool or anything abrasive will destroy the finish.

The chrome steel covers on the forks are just ornamental and can be deleted if desired.

 

Straight vinegar is a good "rust buster" too...
It`ll turn the rust black,
Dennis

 

My 97 Shadow ACE VT1100 wheels looked like yours. I was able to clean them up a bit with steel wool and diet cola. The problem is that the rust never sleeps and will eventually show up and it'll be a constant battle to keep it a bay. Should you ride this weekend or polish your spoked wheels? Eventually I replaced my spoked wheels with 2004 Sabre VT1100 cast aluminum wheels. Problem solved!

 

I have an 00 VT750CD that had oxidation and rust on the forks and hard metal areas (not the air intake cover). What I did was get a few different size wire cup brushes for a drill and sanded the rust and oxidation off. Once it came off I used a polishing brush attachment for drill and used mothers mag and aluminum polish and it came to life. I wish I took before and after pics.
For the rust... get some loctite naval jelly and try using the wire brush or different grit steel wool.