Well, you can simply buy all these fast cars, ofcourse if you have enough money. It is much simpler to achieve in singe player, because after finishing the main campaign each character will receive a huge load of money.
To get fast cars go to your in-game mobile, then open browser and click on Travel and Transport. There you will see a list of websites, where you can make your desired purchase.
For example, legendarymotorsport.net will suit your needs perfectly.
And answering your second question - what is the fastest...I think it is Progen T20.
Anyway, you can get any car you buy to LS Customs and tune it, so basiccally, any car can be fast as hell.