Can we zero rate exported cars/vehicles and claim input tax incurred to purchase them?
I have never looked specifically at car exports before but genrally speaking you can claim back all vat back on items that relate to zero rated sales - so i can't think of any normal reason why not specifically due to the fcat the car is being exported. Note normal caveats ref claiming vat on cars would apply.
Unfortuantely rules for cars can be very quirky - the main issue here i suspect is that i doubt very much that its a given that you will specifically be charged vat on cars you buy - there is a specific term used here that confirm the car is a "vat qualifying car" - most used cars are sold without vat being charged or sold under margin scheme - for both those routes you won't be charged vat.
You also have the additional issue that there are additional restrictions ref claiming vat on car purchases that generally stop any input vat claim being made (even when billed) - if the car is "available for private use including commuting" then you won't be allowed vat reclaim in the fisrt place whether car is exported or not !!
If you do buy an hold cars in stock for exporting be careful how they are made available to be used in the meantime!!
Note as advised at the outset car rules are quirky and somewhat hard to follow even for experienced bods - so small chance i could be missing something specific ref your question.
Ref commercial vehicles - i cant think of any problems claiming vat back on these - same logic applies if sale is zero rated you can claim vat back on the purchase - again be careful to check you have specifically been billed vat - commercial vehicles are sometimes sold on margin scheme and if that is the case you wouldnt have a valid vat invoice.