First, before anything else; pull over to the side of the road whereever you are and shut off the car. Wait about 5 minutes and pop the hood. Now go out and lift hood and locate dipstick and remove it and wipe it off on clean grass or a stick or a Kleenex. Now put back in count 3 seconds and pull it out again and see where the oil level is at. It should be between the 2 notch marks either clear, light brown or black(color does not matter - having some oil does, If the oil is OK. then it is not due to lack of oil pressure or lack of oil.
I know you said ABS and power train; but sometimes the warning lighting seems to get mixed up. So I am just doing the for certains. Now on the firewall drivers side there is a clear plastic canister near a big black disk thing The clear canister should be nearly full of fluid and you can see it from the outside. That is the brakes. If the container is only half full or less the container turns white...showing it is low on brake fluid Dot 3. That has a sensor in it that starts a red light flashing for brakes(you won't have any if it runs out) . So not quite as important as engine oil but still a 1. If you are low on oil then you walk to the store or call a tow truck. Brakes is basically the same deal.
. If engine oil level was O.K. another check you can do on the side of the road is automatic transmission fluid check. For this in most cases the car has to be running in idle and now you know you can run the motor, without damage, then you let the car idle and pull out the other dipstick usually located on the passenger side of the car and up high and it is a long dip stick, wipe it off and reinsert and count to 3 and pull it. and the transmission oil should be between the 2 marks. If it is, then it is not the transmission oil being low. Nor is it overheating.. If you have power steering then up near the front of the engine you will see an alternator, something with visible wiring and on the other side being driven by another belt is a canister with a removable twist top . Undo the top. It has a short dipstick It is a wipe and stick in while engine is still idling and then remove and look at the short stick for fluid. If there is no fluid then you need fluid or your power steering will quit and it becomes arm-strong steering. You can drive it but steering around corners may become harder. You are safe to go back to the dealer and see what he can do for you. Usually this is no "skin off their nose" so should be happy to comply with the request...as YOU are not the only customer they sell cars too and they DEFINITELY DO NOT NEED A BAD ASSESSMENT VIA THE INTERNET...AS THEY have selling cars as their business...and want to keep the public happy and a bad REVIEW IS BAD BUSINESS for them.
I would go back and see the same dude that sold you the car and hopefully you are on friendly terms(as he just took your money) so, state there is a "problem with the car and would his mechanic be able to look into it FOR FREE. Because you did less than 10 miles. and all hell broke loose. Now the used car dealer may have somebody around to help fix the car for the simple problems.
. I mean, these are the simple checks you can do to make sure the car makes it back to the dealer without BREAKING DOWN COMPLETELY...and easily fixed. Otherwise you got junk...and they will not even look at you, because now something is definitely broken. or Costly.
40+ year auto mechanic.