Q2: Is it right to transform this sentence
"Because he was shot dea, his dictatorship is over." into "Being shot dead, his dictatorship is over."?
I would suggest instead "Having been" for "Being."
In this case, "Being" is better suited for a condition, while "Having been" works better to say he was the recipient of an action.
However, in both cases, what follows needs to be the noun described (he) not something related to that noun (his dictatorship).
Being dead, he was no longer the dictator.
Having been shot dead, he was no longer the dictator.
(Both of those sound a bit like Monty Python, though. Most people would assume that dead people aren't able to rule in any capacity, elected or self-appointed.)
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.