Fantastic car!!

There isnt anything that you shouldnt be using per say, but certainly perhaps in moderation - for example; give that the paintwork has been mopped or polished previously, and perhaps you dont know how many times, it would be impossible to say what amount of paintwork is on the car without a depth gauge. So if you were thinking about going at it with a machine polisher, even a Dual Action, I would proceed with caution.
With tar removal I would seek out the better products for doing that sort of work, just to be that be safer. There are some very aggressive tar removers from the likes of Halfords, etc, such as Holts Tar Remover (aerosol) which your paintwork wont thank you for.
As said, keeping to the likes of pH neutral products will help with keeping the paintwork fresh. Given the type of paintwork it is, you will need to lightly polish it to keep it from oxidizing, and doing so by hand will have minimum impact, but restore the deep shine quite easily.

Depending on how bad the cloudy marks are, as mentioned the likes of Autosol or Meguiars NXT Metal Poylish will do a good job with a bit of elbow grease. Something worth considering is getting them back to a good condition and sealing them with a durable nano sealant such as CarPro DLUX (which can be used on fade black trim also) or Gtechniq C5 Wheel Armour. This will ensure very good protection against the elements and thus the clouding, and far easier to wash them. There is a bit of prep work involved, so that needs to be considered also. Then there are traditional type wheel sealants, Chemical Guys Wheel Guard or Poorboys Wheel Sealant that will helps, but nowhere near as durable. 1 year plus for the nano types, versus 2-3 months of the traditional type.