The ID is sufficient.
No visa for the countries of the European Union: valid identity card or passport.
From my petsonal experience, yes you can cross the passport control with your wife + marriage certificate + your passport + your residence card in romania
Practically citizens from all the world can travel in Romania; for details ask the Romanian embassy in your country or see the link below.
Yes, as long as the felony does not contradict the romanian police records (a robbery is ok, but a terrorist attack is not)
Yes.
Yes, it is necessary.
For a Greek citizen: identity card or passport.
no
An identity card is sufficient.
No, you need a valid passport.
Yes you can, but you need to apply for a visa issued by the Mexican government.
Yes, because Romania and Spain are members of the European Union.