The DC3 flew and was in service by 1936, even the DC2 was an excellent aircraft. The best hope the Germans might have had was a He 111 with the fuselage physically widened out but using the same wings and empennage. similar to how the DC2 became the DC3. The great economies of production then make the transport viable and as the He 111 bomber was superseced production could shoft to the transport version. One then ends up with a conflict between He 111 bomber production and He 111 Transport production. The bomber would tend to win in the early part of the war. One might have to put radials on that He 111 Transport to spare Jumo 211 production.
Given the development timing of the Fw 200, and its wide (3 seat row) fuselage design, having a smaller twin engined counterpart using a similar, but shorter fuselage and smaller wing and tail (like the Fw 206 later did) would have made sense to develop in parallel with the larger trans-atlantic airliner. (and far more likely to actually be profitable ... or close to it -let alone strategically useful as a mass produced military transport)
I suppose the same argument could be made for the Ju 90's development though. (perhaps more so given its greater passenger capacity than the Fw 200, though also possibly better in a shortened tri-motor arrangement rather than a twin)
But yes, the He 111 seems one of the better options as well, and in development earlier than either of the above. Its design is closer to the Lockheed Model 10 or Model 14 than the DC-3, but it also had a much larger wing area and possibly more potential fuel capacity and perhaps even more potential than the Model 14 to be stretched/expanded as the case with the Lodestar. (granted, the Passenger He 111 only had the capacity of the Model 10 as it was, so it could use all the expansion it could get)
As far as engines go, the Jumo 211 has an advantage in drag and specific fuel consumption compared to the BMW and (especially) Bramo radials along with significantly more take-off power than the former. But given the number of designs (particularly transports) that resorted to using Bramo 323s, that seems the likely alternative. (especially once the 2-speed supercharged models are available in number -let alone C-2/C-3 rated ones or MW/50 equipped models)
Yes but who was thinking of resupplying whole divisions and even armies enough so that they would write a spec. There were some superbly thought out airliners planned (they often appear in Luft46 style aircraft) but they would have started production in the war years. Aint going to happen. Even the Ar 232 was effectively cancelled.
Any transport would need to be in production by 1937 else it comes into conflict with military priorities I would think.
Larger numbers of Ju 90s and Fw 200s built used as transports wouldn't have hurt either, but more cost effective 2 or 3 engine transports should have been the priority.