That's a nice looking bike!
The rust on the front derailleur should clean up nicely with a little metal polish. I've dealt with worse, and they usually bounce back. A good cleaning and tuning will probably be all that's needed, as long as the parts aren't totally shot.
Gearing - multiply the number of cogs on the back by the number of chainrings. It looks like a pretty close ration freewheel. If the teeth are worn out, it should be replaced. It looks like it's an older freewheel style, as a opposed to a modern cassette.
Wheel hubs - You could probably just rebuild them. I have no experience with Campy, sadly, but they are known for being rebuild-able. Take them apart, clean them up, replace pitted/worn parts, fresh grease, reassemble. If they run smooth, i would probably just keep them as is.
The Shimano front derailleur - You're mixing Campy and Shimano?!?!! Someone's going to have a heart attack!! Seriously, though, i'm guessing the shifting is all friction, or at least the front, so functionally, it shouldn't be a problem. If you want to convert it to index shifting, you'll want to get compatible shifters/derailleurs, usually the same brand/style/speed. With friction shifting, you can mix and match. To replace it, get one with the same clamp diameter so it fits your frame, and one that can handle the same jump between the chainrings.
As long as you're stripping the bike, check the headset and bottombracket. Clean, inspect, grease and rebuild. It should be good.
Again, awesome bike!!! Have fun with it.