Getting all those checks done is the whole point of using the specialist. They have a reputation to maintain so it's in their interest to ensure all is in order.

With regard to warranty, the remaining balance of the manufacturer warranty is transferable. Some dealers in UK will do some sort of support if you buy & export, depends on the individual deal. You can also use the removal of a warranty obligation as a bargaining chip to reduce the price.

People like Dream Cars can offer a warranty (at extra cost), usually through someone like Mapfre or Mondial. These can be very restrictive. You can also arrange this type of warranty yourself, they start at around €400 but before you jump for this you need to read all the fine print as they are notoriously restrictive in terms if what is required.