Hi Grainne; Welcome to the wonderful world of Rocket heaters!
1) This is easy , a rocket mass heater is a rocket stove heating a mass. A Rocket mass stove is the same thing.
However a Rocket stove itself is just the core burner assembly without any mass.
2)Yes, easily as a stove top.
3)Yes, as a stand alone water heater it can be easily done. Trying to combine it with a home heating setup would be an issue.
4)A small brick bell batch box might be more to your liking but in some applications a well built box stove can be the right choice.
5)This is a slightly harder one. Yes it has been done. Usually not in city limits (at least not legally) Thru the roof is always better , but yes you can go out the wall and up. BUT you must use expensive insulated chimney pipe.
Ask away Grainne, we have lots of cheerful rocket scientists eagerly awaiting your questions!
EDIT) Here is a link to a master builder. Matt sells plans for some outstanding heaters. You might be very interested in his tiny house cook stove and his new water heater!
http://walkerstoves.com/