They had gone through a massive reorganization that was still ongoing after the official position that 'Deep Battle' doctrine wasn't in political favor anymore in 1939 and in the wake of experience gained in Poland, then they reorganized right after the lessons learned from the German victory in France, which mean the MC only showed up again on paper in late 1940. They were only starting to get close to TOE by June 1941, but weren't really even ready to fight then, while even at TOE they were woefully short of truck support to make them function well in combat, a lesson the Germans learned the hard way in 1940, which in part was the reason for the 1941 Panzer division remodel that halved the number of tanks per division while maintaining the same number of trucks. The Soviets too learned the hard way in 1941 and remodeled their tank divisions/corps later in a very similar way to what the Germans did after 1940.
You are conflating quite a few things there. Horse supply was a small fraction of what the overall lift capacity of the German army in 1941, because it took a lot of horses to equal the capacity of one truck, while having a bunch more limitations on how much rest, food, and medical care they needed. So horses were limited to very specific roles within the 1941 invasion force, namely supply/weapon haulage for foot infantry divisions. The fully motorized infantry and panzer divisions did not have horses and were much more mobile, which of course led to a lot of problems of them outrunning the foot infantry divisions in 1941, while horse die off during the campaign caused quite a few other problems.
Source on that. I think that number was entirely for all automobiles of all types, not just trucks. Plus a lot of them were required for industry/commercial use.
https://en.wikipedia.org/wiki/Automotive_industry_in_the_Soviet_Union#Early_Soviet_period
Yeah looks like 1938 was the year and it referred to all motor vehicle production that year, not just trucks. Plus there was a major downturn in motor vehicle production after that, so production in 1940 was lower than in 1937.
This is true, the question is what could the Soviet industry actually produce, especially if the British effectively do put Baku out of commission, as by 1940 it alone accounted for about 60-70% of Soviet oil production.
That structure wasn't even ready in 1941. They only just started after France fell and they realized their mistake of disbanding the mechanized divisions of 1939. Quickly assembly of units on paper doesn't tell us anything about their ability to operate. They won't really be operational to use in the Middle East for quite some time. They could of course focus on getting 1-2 ready ASAP and forget the rest, but honestly given the terrain and Soviet affinity for cavalry, they'd just use cavalry as their fast exploitation units as in WW1 in the region. It seems based on WW1 history of the Caucasus/Persian/East Turkey campaigns that cavalry were extremely useful and effective in the area and probably would be more so especially early on until supply routes are secured to flatter terrain and mechanized units could actually operate in terrain that was more conducive to their operation. Frankly I think the British and French would have a LOT more to worry about from masses of Soviet cavalry, which they could and did use effectively IOTL. An early version of the cavalry-mechanized group seems quite likely and would probably be very effective in the region. The Allies IMHO would have been foolish to poke the Russian bear in 1940, as they'd likely lose the resulting ground confrontation in the region.