Great topic, I until June this year spent 15 years selling cars and without the various finance products behind you as a dealership it'll be a struggle to survive.
Re VT yep as already said its your right (known as halves and thirds in the trade) and of recent years more people have exercised the right their legal right to VT their agreement, in many cases now many finance companies now save a dedicated option on their customer facing phone menu when you phone them due to the ramp up in volume. It won't of course be something on the agreement that'll particularly stand out in terms of clarity but it is your right and with all the information available via the web and various consumer programmes/organisations the finance company's are in the main paying this area of the finance agreement the attention it deserves.
Re whether it effects your rating or credit line in essence no it doesn't, it can't. However I was told a good few years ago that it will be seen/looked at by a finance company should a customer apply. But of late finance company's want business that's how they earn their crust and they've in the large moderated their view as to whether to lend to someone that on record may of even the past simply exercised their right. But if he customer was seen/is a serial VTer then would you lend them money in the knowledge that you won't see the loan paid back in full and you'll get a depreciated asset back on your door mat to off load as well?
Think about it as a consumer you're going via the dealership/lease company going to them with a view of asking them to lend you capital against an asset that'll depreciate, they'll look at the application and lend accordingly. There's a view that they don't if they don't want to have to advance you the funds if they(the underwriters)perhaps feel that they may not get back the whole agreement in terms of payments/interest as that's how they'll calculate what lending the money to you and I will net them overall.
Re agreement types quite a few companies over the years have created new products to assist them selling finance, you can as explained obtain a HP agreement with a balloon there are now longer term PCP agreement up and above the normal run of the mill 24 & 36 month agreements.
When buying the car at some point you'll be steered into the jerky world of funding(will you be using our bank or yours might be the question you'll be asked) and it'll be driven by a conversation in terms of rate(easier when selling to convert customer to dealer funding) or by product certain products will earn the dealerships more money, for instance the last dealership I worked for was paid £300 for each agreement on PCP we signed up (known as a document fee) and that was at 5.9% which if you think about it is about average these days so what's in it for them to pay a dealership that sort of money especially as being a low rate the return won't exactly buy them a yacht on the returns. Put simply if we as a dealership have done our jobs right then chances are we'd see the customer back again for a new car tales the car in or trade in we'd re sell it and if the finance agreement was sold/handled correctly them we'd have another finance case next time around and it goes on and on. It's how we all survive.