Welcome to your Baptism by fire on the 6.0
That white smoke was telling you to stop driving the truck and fix it.
That missing coolant was also telling you to stop driving it.
Here is what happened before your no-start:
The oil cooler is plugged in the coolant passages within it (liquid/liquid style cooler). This will slow the coolant flow to the EGR cooler (EGR cooler gets its coolant supply from the oil cooler).
This slower moving coolant allowed the EGR cooler to overheat, and it failed internally. That failure allows coolant to flow out of the egr cooler and go one of two directions when the engine is running.
One is into the air intake when the egr valve is commanded open by the PCM. As you can imagine, pouring coolant into the combustion chambers is a really bad idea. This can result in cylinder pressures than the stock head bolts can withstand, and they stretch, followed quickly by popping the head gaskets.
The second direction the coolant will flow with the engine on is out into the exhaust. This will eventually cause your turbo vanes to stick, since the coolant is entering the exhaust system previous to the turbo and flows through the side of it that contains the vanes that control the boost. Add uncontrolled boost caused by sticking vanes and higher combustion pressure, and you are surely headed for head gasket replacement.
When the engine is off, the leak does not stop. The coolant will still leak out of the egr cooler and build up behind the egr valve, just waiting for it to open and make your engine gulp a big gulp of coolant. The other direction, since there is no exhaust flow to move the coolant upwards towards your turbo, it will flow downwards into the passenger side exhaust manifold. If there is a set of exhaust valves open on that side of the truck, the coolant will flow into that cylinder and fill it. When you climb in and turn the key, you just hydrolocked your engine.
You might not have popped the head gaskets yet, but I would bet that they are most likely gone by now.
At an absolute minimum, you are looking at replacing the oil and the egr cooler (or deleteing the egr cooler). You are most likely going to have to replace the head gaskets.
DO NOT use the stock head BOLTS again. Use ARP studs as a replacement, you will not regret that.
Use the stock FORD head gaskets. The gaskets are not the issue, the stock head bolts are.
When the head come off your engine, they MUST be taken to a machine shop that is capable of milling/rebuilding/checking these heads. DO NOT allow a FORD garage to tell you that they will handle this for you. Their procedure for checking the heads is not nearly good enough for what must be achieved. The machine shop must check flat/straight. If they must mill the head surface (likely they will have to) they can not remove more than 0.008, if more needs to come off, you are buying a new head.
If the machine work is done the right way, ARP's are installed PROPERLY, you use FORD gaskets, and delete your EGR cooler, you will never have to worry about another head gasket as long as you own the truck. Ignore something....well, you get the point.
There are 3 links in my signature line that will interest you. The first is a link you should have read long ago, before considering buying a 6.0
It has a bunch of info a new 6.0 owner needs to know, especially what gauges are REQUIRED on this engine, what they should read and what to watch out for.
The second link is a flushing process to rid your cooling system of the junk that caused all of this mess you are in (ignore all of the "reverse flushing" part of that document, it won't help you one bit).
The third is all about replacing the egr and the oil coolers.