6/3 NM-B is not wire, it is cable. Cables contain multiple wires. NM is fine for running through ceiling joists in dry areas where the cable will be protected. If water is involved in any way, you need UF cable.
Cable can be run through conduit, but only if you are a masochist. It will be a rather difficult pull. You will need much larger conduit, because the conduit fill is calculated by looking at the widest dimension of the flat cable, and imagining a round wire that diameter.
There's an exception that allows this imaginary wire to fill most of the conduit if it is the only cable in the conduit. But that only makes it an even more difficult pull, and paints you into a corner as far as any future use of that conduit.
You cannot unsheath cable and use the individual wires. That is because the individual wires do not have individual wire markings to disclose their type and grade of insulation, and generally their insulation is not tough enough to survive any type of use outside a junction box. They are allowed as short pigtails entirely inside junction boxes.
If you find cable whose interior wires are marked as some sort of wire that is legal for use in that application, then have a field day. This is rare but not unheard of, talk to your local electrical supply.
You cannot do a continuous run with new wire because you cannot use loose wires in through-joist wiring. You need to either fit conduit in the joists, or use some sort of cable rated for such use.
If you run all metal conduit, that is one less wire you need to carry, as the metal conduit serves as the ground wire.
Before you decide on the romance of continuous wire runs, count your bends. More than 360 degrees of bend between access points is illegal. More than one makes pulling exponentially harder.
It is very easy to build a conduit route that is so difficult to pull that you end up needing to call a professional to do it. Professionals don't like doing a small part of the work, and will want a big chunk of the total job. Access points are the key to avoiding this, but of course, access points are the enemy of "a finished look" for some reason. I don't know why, the Victorians had no trouble fitting adorable cabinets where utility access was needed. It is a 20 minute job to change my tub faucet. Really.
Attach to the wall and the back of the parapet. Drilling holes in the flat or sloping parts of a roof can end in tears down the line.
Consider passing the wire through the parapet instead of over it.
Conduit joins welded using the correct method, solvents and glues will not leak.
you probably don't need an expansion joint, just don't put a bracket within one foot of the corner (allow the bend to flex as the expansion joint)
Best Answer
I've only seen liquid tight with threaded connections, like this:
So basically you need to go from 1 1/2" to 1/2" threaded.
There are reducing bushings, like this:
Finding 1 1/2" to 1/2" seems to be difficult (that's a big drop) -- but they do exist (I can find them in catalogs, just can't find an actual picture).
If you can get a 1" or 3/4" to 1/2" (much more likely) then you just also need a reducing bushing (or two) to go from 1 1/2" to that size:
Another way to make the connection is to use a 1/2" female adapter on the end of a short piece of PVC pipe:
Again, you'd have to use bushings to get from the 1 1/2" box to the 1/2" PVC pipe.
Be sure to use PVC cement to make the connections and keep it water-tight.