1. Yes, bouncing a check is regarded as a criminal offence.
2. Possibly, depends what communication there has been between the banks and/or the police in the two countries.
3. I think individual countries issue arrest warrants for within a country but I guess the UAE police can request the police in another country to issue an arrest warrant?
4. I would assume there is some sort of communication between the GCC countries whereby immigration of one can or might notify police/immigration in another country.
5. I'm not sure what extradition arrangements there are between the various GCC countries. It might vary between countries and depending on the offence. I would suggest contacting a lawyer and/or the police in the respective countries.
There's another topic with a similar discussion here: UAE entry restrictions when blacklisted in other GCC country