Are you sure the white smoke wasn't just fog from it being cold outside? Does it still smoke? You can look inside the radiator for signs of oil, as well as look at the oil dipstick and under the oil fill cap for signs of coolant(it'll look like chocolate milk), but it doesn't always mix when a headgasket blows, sometimes the gasket fails in a spot that allows the coolant to flow out of the engine without mixing with the oil. The only way to tell for sure is by doing a cylinder leakdown test. AutoZone sells a kit for about 30 bucks. This will tell you for sure if you have a blown hg. I suspect it wasn't bled properly or maybe the engine had been overheated in the past and this last issue with the coolant fitting was just enough to push it over the edge. At the very least, you should try bleeding it yourself. Maybe the gasket isn't blown and you might of gotten lucky and caught it in time.
Now here's a possible answer to your coolant level issues. When there's air in the system, it does all kinds of wacky stuff to the coolant level. The cold boiling you speak of may not have actually been boiling, just thousands of air bubbles under pressure. When you have airlock(radiator fills with air and prevents coolant from circulating), the coolant in the engine has nowhere to go. It evaporates into steam and builds up pressure. This can also damage your temp sensor, fan switch and thermostat due to extreme heat. So how does air get into the system? Well there's two ways. One way, is when you open the loop to change a component such as a thermostat, water pump, plastic coolant fitting, radiator hose or radiator. Coolant drains out and when you try to fill the radiator back up, the air void has nowhere to go until you bleed the system. Even then, it takes several tries to completely bleed all of the air out. Once is simply not enough. The other way air gets in the system is through a leak. A cracked radiator will not only allow coolant to leak out, when the coolant is gone, you have nothing but air left to fill the void of the lost coolant. I suppose air can also get in from wherever the leak is whether it be a blown hg, cracked radiator or leaking coolant fitting. Think about it this way, when you take a bottle of water and dump it out, what do you have? An empty bottle right? Wrong, you have a bottle full of air
So, how could you tell if you have a coolant leak? You can't always see where coolant is leaking from. Sometimes the leak is so small, the coolant evaporates as soon as it comes out. Or sometimes the leak is in a spot that is hidden and not visible. I had a hairline crack in my radiator right between the radiator and expansion tank. I couldn't see it because the expansion tank was covering it and the leak was so small the coolant was evaporating before it could drip down the side of the radiator and onto the ground. One way to find a leak is to park the car in a quiet location such as a garage or in an alley between adjacent buildings. Then you're gonna want to wait for the engine to cool, never remove the radiator cap when the engine is warm. Then you'll need to pressurize the system. I rigged up a cap that threaded onto my radiator to a bicycle pump. Pump it up to about 5psi, no need to go over 7 or 8 psi. Once the system is pressurized, stick your head in there and listen for hissing.
All that being said, I remember a few members having problems with the plastic coolant fitting that your mechanic replaced. I believe the brand sold by pelican parts(maybe other vendors as well), were not a perfect fit and they leaked. You definitely want to make sure you get Genuine BMW Parts.
It sure sounds like you still have air in the system. You may have a blown headgasket, but don't just take your mechanics word for it. In fact, don't even let him mes with it anymore. They might just try to "make" your headgasket fail so they can get more work/money out of you. Do the leakdown test yourself, it's pretty simple. If it checks out good, follow up by doing a PROPER BLEED:
1) Park the car on an incline so the front is raised
2) Allow the engine to cool
3) Start the engine
4) Turn the heater to full hot(red)
5) Turn the blower on full blast
6) Remove the bleed screw on top of the radiator next to the radiator cap
7) Remove the radiator cap
8) SLOWLY pour coolant into the radiator expansion tank through the FILLER HOLE(not the bleeder hole)
9) Continue filling the radiator to the top until you see a steady stream of coolant coming out of the bleed hole. As you're filling the radiator, tap and massage the radiator and hoses to encourage any trapped bubbles to make their way out of the bleed hole
10) Once you see a steady stream of coolant WITH NO AIR BUBBLES, replace the bleed screw and radiator cap
11) Drive the car around the block, allow the engine to reach operating temp(12 o'clock on the temp gauge)
12) Park the car on the same incline
13) Allow the engine to completely cool
14) Repeat the same process several times until you feel HOT air coming from your dash vents
Follow these steps PRECISELY and in this EXACT ORDER. I can't stress enough how important it is to bleed the system properly. No matter how many times I post the instructions, people always seem to screw it up. I wish BMW would've made a big yellow sticker and attached it on the radiator cover. It would've saved thousands of people from replacing motors due to headgasket failures. I hope that helps man. Best of luck and lets keep our fingers crossed that your hg didn't blow.