There's quite a lot here, so let me break it down into different aspects. When buying a used car, the 2015 Consumer Rights Act theoretically gives you the statutory right to reject a new or used car (or anything else) within 30 days of purchase if any fault is found. According to the act, goods must be of satisfactory quality, fit for purpose and as described.

Satisfactory quality: The car should be of a standard a reasonable person would expect, taking into account factors such as age, value, history, mileage, make, durability, safety and description.

Fit for purpose: Fit for purpose means that the car must be usable for the purposes that you would normally expect.

As described: The car must also be as described. This means it must fit any verbal or written descriptions which the dealer has provided.

As you can see, there's quite a lot of room for interpretation here and the act is untested in this area. I would make sure the car is inspected before it is purchased as this means you can then decide whether or not you wish to go ahead with the sale - rather than buying the car and then getting it inspected. As with anything, take as many notes as you can of conversations with the dealer (not a problem if you've used email - but can be tricky on the phone).