I think there is a lot of potential, but I clearly don't like this civ in its current state.
You essentially play with no bonuses for a good part of the game. Your UB is bad, as you will use only half of its bonus (either the bonus on puppet CS, either the bonus on ally/friends CS), since declaring war twice to CS give you definitive diplomatic penalty with them. Moreover, you will not really use the diplomatic units with this civ... Your tanks are kind of OP in the right situation, but they are quite late so they're just useful to confirm a victory.
Moreover, this civ is crap as an AI, as even if you feel threatened by them, you can just take the same ideology and they lose their OP promotion against you.
I don't see a lot of cases where I wouldn't prefer the Mongols over this civ.
Suggestions (feel free to ignore some or all of them):
UB change: Also count CS that are afraid. Give a unique promotion to envoy/.../diplomats so that they are useful even after having captured all the CS. [not sure what promotion, though]
UA replacement: All improvements have -1 food and +1 prod. Puppet cities gain happiness like normal cities. Free Courthouse when capturing cities (puppet or annexing).
UU change: I would add a bonus against cities.
Alright, I'm proud to see that people at least like the concept of the concept. I've been thinking a while about changing the UU and although I don't have the specific stats down, I have an idea to make it good.
UU: IS-2 (replaces Tank):
-3% production cost.
Ranged Combat Strength: I don't know what would be balanced, please suggest.
Range: 1
Combat Strength: This might need to be lowered from default a slight bit.
Starts with promotion, "Overwhelming Numbers"
Overwhelming Numbers promotion:
Subsequent attacks by an IS-2 against a single unit during a turn are ranged.
May attack units of a civilization with no ideology or differing ideology twice, first attack costs no movement.
Promotion is lost on upgrade.
The first part of the promotion doesn't necessarily have to be by the the same unit, so if you just have a bunch of IS-2s on a frontline, even on somebody with the same ideology, you can absolutely wreck the numbers with very little damage against the tanks. At least that's what I think would happen. My justification for this is that the IS-2s overwhelmed enemy forces so much that they could not defend against their attacks.
UB: Commissiarat (replaces Chancery):
2 maintenance (down from 3).
+1 Gold and +2 Production per puppeted or afraid CS.
Grants a free courthouse if built in a puppet.
Grants Promotion, "Red Terror," for Military Units in the city in which it is built.
Red Terror promotion:
May attack CS units twice, first attack costs no movement points.
Ignores CS ZoC.
This obviously requires a change to the UA (since the UB now does what part of the UA did). I'm not a fan of your UA suggestion because I think this would kill early game growth and likely necessitate micro-ing tiles (and one of the reasons I wanted a puppet civ that could settle cities is because I prefer to puppet, but that's a nightmare on happiness).
I will replace the "Courthouses are instantly built in puppet cities when annexed with no buildings in queue" with something else since the UB already has that down. I should probably borrow from early Russian history (before the revolution). Does anybody have any idea of a UA addition that will not encroach on any other civs UA? Maybe conquering a city starts a half-golden age (6 turns instead of 12). I don't like that since it feels like a better French/Aztec UA. Maybe the Red Terror promotion grants +1 movement if on a different continent to the city it was built in (to represent the Soviet Union being a world superpower getting involved in affairs all around the globe)?
EDIT: I just want to be clear that I liked your suggestion of the UB granting an additional promotion to diplomatic units so that they are still useful in a game without CS. I just don't have an idea for a promotion that is both interesting and not overpowered. Maybe diplomatic units grant a buff to nearby military units, like a great general, based on the amount of puppet CSs.