I’m not sure Carfax can be trusted as to the date it was put in service. Likely true, but it could have been sold at the end of 2014. Sold earlier, then that’s when the 8-year battery warranty starts. The Tesla App will show the correct warranty date, but I suspect you will not see that until you own the car.
Odd that unlimited SC is not included. I suspect the car was bought by Tesla and sold at auction without Lifetime SC as only Tesla can do this. Tesla can’t remove Lifetime SC except for salvage vehicles and used ones they bought and elect to resell. Nothing wrong with that, but just so you know that it doesn’t have Lifetime SC so it is not misrepresented what you’re buying.