Long story short I bought a 2003 Mini Cooper S to build into a fun car and learn about working on my own cars. In the short time I've owned it it has definitely given me lots to work on. Today after getting the car warmed up, moved, and ready for my first time doing the front end service mode I noticed the car was smoking quite a bit. The car has an oil leak coming from I believe the back side of the engine, but I can't really see the origin of it yet. The coolant tank at the back of the engine was completely empty (it had coolant when I first got the car). I refilled with Zerex G05, which is what the previous owner used. I started the car back up again after refilling the coolant tank and it had a tiny bit of smoke coming out of the coolant tank.

Could the oil leak, missing oil, and smoke in the coolant tank be related? My first guess would be a head gasket if they are related, but I'm still trying to learn these things. I'm still going to put it in front end service mode, but I'm still not sure that would help me see where the oil leak on the back is originating. I welcome any suggestions on what to look or possible causes.

 

I'm learning as well, so take my advice with a grain of salt.

All those could be symptoms of a blown heat gasket, but that would mean it's blown in several places (oil jackets <=> outside of engine ; coolant jackets <=> combustion chamber). Also don't jump to conclusions about blown head gasket, it could be any number of things, so diagnostics are required to ascertain it is.

For the oil leak/missing oil (which is likely the same issue), first would be to trace where it comes from. Did you consider moving coolant / power steering reservoirs aside to have a better view of the back of the engine? Also using a mirror to see better. You could also push aside the heat shield below the exhaust header. It's hold in place by a single 10mm and there is room to push it aside (that's how you get the starter out). If you still cannot see it, the next step is probably to use a UV dye.

As for the missing coolant an smoke coming from the coolant tank, the first thing to do is to test if that smoke is exhaust smoke. If it is, you definitely have a blown head gasket. If not, you gotta dive deeper. There are test kits available for about $20 to test that, search for "Head Gasket Tester Kit".

Do you have other telltales signs of a head gasket failure? White or blue smoke coming out of the exhaust, or the engine overheating before issues started?

Front-end service mode won't help you see a leak coming from the back of the engine. It gives access to parts that are in the front of the engine (radiator, fan, water pump, AC compressor, alternator ...).

 

This car started to have issues upon driving down my driveway (not an exaggeration) so I haven't had it on the road enough to even get to know it. The car does have white smoke coming out of the exhaust. After pulling off some of the panels/fender well and getting the car up on QuickJacks I see that there is oil and grime pretty much all over the back of the engine and down the passenger side of the block. There is also a small leak at the front of the block around a sensor. It's so grimy and dirty back there I'm not sure where it could be originating just on visual inspection. A lot of it is around the oil cooler, but there is too much in front and above it to just be that so I'm going the UV Dye route so I can better see where the current leak(s) may be.

 

Grime and dirt could be from a previous oil leak that has been fixed but from which the oil has never been cleaned, and now it's just dry oil grime (I have that on my car, it's dirty). On the other hand, if it's wet or even if there has never been an oil leak (or if it was cleaned before), yeah it's a giveaway.

White smoke coming out of the exhaust is a really strong indicator of coolant being burned during combustion though (unless it's just on warm-up because the car is cold, but I assume you know the difference). Using a head gasket tester kit would be a good way to ascertain that, but coolant level dropping + white smoke + smoke in the coolant tank => all that makes me 95% certain it's a blown head gasket. Using a tester kit would bring this to 100% certain if it's positive.

If you go ahead and start fixing the head gasket situation before finding the oil leak location, a visual inspection of the head gasket could let you know if it's coming from here as well.

Please note: I've said "blown head gasket" before, but the proper description is "blown head gasket and/or wrapped/damaged head". If you go ahead and start pulling the head to replace the head gasket, you'll have to check the head for wrappage or any other damage, and possibly have to machine or even replace it. If you want to have a look, that's what happened to DIY Youtuber "The Savage Garage".