Yes but make sure that you get it completely serviced and checked for everything like brakes, engine oil etc. Is it a very old model of Nissan Sunny?
You can get hotel rooms once you land there.
Going from Doha, it may take 20 mins at Qatar Border and may be 30-40 mins at Saudi border.
Route would be Salwa border to Hofuf then Riyadh(via touching Dammam border) and then 900 Km to Makka Al Mukarram. Total journey is about 1400 to 1500 Km.
Following Al Haram sign from Riyadh would be enough.
There are service stations from Doha to Mecca like SASCO, Tesheelat, Aldris etc.
Better to start immediately after fajr.
Yes there are hotels, rest houses between Riyadh and Mecca.