!999 Grand Vit- sounds like it's bottoming out, esp when turning.

Just a thought if it is running rich to high fuel mix
How To Find A Vacuum Leak - EricTheCarGuy
https://www.youtube.com/watch?v=9CPqbaSgcok

2003 Suzuki Grand Vitara - Problems, Statistics, and Analysis
http://www.carproblemzoo.com/suzuki/grandvitara/2003/

If the exhaust smoke is black:
Clogged or dirty air filter, Bad fuel pressure regulator, Leaky or clogged fuel injectors
https://www.yourmechanic.com/estimates/suzuki/grand-vitara/smoke-from-engine-or-exhaust-inspection

SUZUKI GRAND VITARA SERVICE REPAIR MANUAL 1998 1999 2000 2001 2002 2003...

for the best solution of your problem visit this site

this document might be of help
http://ww2.justanswer.com/uploads/PENTICO/2010-03-19_012354_suzuki.pdf

take the donut back off

Valve covers leaking oil OUT the tail pipe, no way in hell! Valve covers can leak oil onto the exhaust manifold, but there is no way its going to get into the exhaust from there and out the tail pipe.

Bad valve guides and/or valve guide seals would put oil from the top of the head and into the cylinders. That is a far bigger job than just replacing valve cover gaskets.

Don't let the warranty company give you any more of that kind of BS.

If jumping the car off starts it and it will keep running, then you have a bad battery and need to replace it. If it starts the car and it shuts off again, you need to replace your alternator.

As for the oil situation, make sure there isn't an oil leak. And it isn't likely that there's an oil sensor.

There is more than one seal on a car. But, having said that, the first place I would look would be at the rear main seal area - where the crankshaft leaves the engine. This you won't be able to see directly, and you want to be very sure that it IS leaking before you start because the gearbox and transfer assembly has to come out first. Or you could remove the engine! There are at least 3 other oil seals and a number of gaskets and hoses that could also be the source of your problem. You have to describe where the oil is leaking from.

Blue smoke come from burning oil.  This means that you have an oil leak somewhere that it is getting burned up and exiting the muffler.  First thing I would do would be to check your engine oil level.  After you are sure that it is good, I would suggest taking the vehicle to a mechanic to have them see if they can find where the leak is.  Let me know if you have any other questions.  Thanks for rating my response and for using FixYa!

this would more than likely be cause by a bad cylinder head gasket. I would bet 89% this is your problem.

Hydraulic leaks are typically a result of seals/o-rings wearing out. If you gave a leak coming from the cylinder you will probably have to replace the cylinder. Unless you are can do the repair yourself its unlikely that you will find someone who can rebuild it for less than a new one costs