To keep things equal as possible & who ponies up the $$$
Way too many oil choices out there, plus they give the oil to the Teams. Fuel & Tyres are purchased by the Teams.
No, the early days they would use the same tyre one could buy at Sears or whoever in the Drivers mind had the best (longest lasting) tyre. Not uncommon for 40,000 mile tyres to be purchased on a Friday, raced all weekend and taken back to the store for warranty replacement because they were worn out.
That lasted till the stores figured out what was going on.
They would run the same set all race weekend. There were cases when Teams would go to the parking lot if needed and get tyres of a parked car/truck.
They also tended to use truck tyres over car because of more plies (6 or 8 vs 4) and they were Biased not Radial.