rx8 noob but no noob to spinning wrenches
 

So I'm here helping a friend out with their car. They have a full household and they are down to one car. Wanting to help get a second car on the road for em.
personally I'm used to pistons. I have a 76 dodge dart with a slant six, 03 Toyota corrola, 05 grand caravan, 91 gmc Sonoma. I also have a 78 b100 van I'm tearing apart for parts even tho I may rebuild it stronger than I got it lol. Anyways...
so this rx8 I'm trying to get back on the road won't run long my buddy tells me. He said he had a new timing belt installed and since then it doesn't run very long before shutting off.
so I get it started and it sounds rough. So I check the oil and literally there is barely a drop at the very end. Which could have been pulled from the side of the tube from the oil splashing up. In no rx8 guy but could running no oil and not having proper pressure cause the computer to shut down so it doesn't destroy the motor. Now I don't know how long they drive like this. There is much showing leaks underneath so I'm unsure how bad the leak is.
i did hook up a code reader to the obd2 port and it shows nothing which does not surprise me as the battery was dead when I got to it and had to jump it with my van.
could it be just need oil and a good brake stomping to get the dsc to start reprogramming itself.
​​​​​​​i did notice a slight coolant smell after it was on for a few minutes and tapping the gas created a bit of white smoke out the tail pipe. In a normal car I'd suspect head gasket failure or worse. Then again I've worked on a caddie that when the mass air flow sensor wasn't plugged in proper would have similar issues with the smoke
i do know there is a possibility of fuel pump failure but the fuel pump sounds strong when put in the on position before starting. I only say this cause looking at trouble shooting, the only solution that comes up to a rotary dying out of nowhere with out and crazy sounds is a fuel pump. I'm also wondering if the timing could have been installed improperly. Any advise would be appreciated

You can only set the timing one way.

Might try try to check for internal engine coolant leak?