Andruil, I like digging for information on the Patriot yet I'm finding very little help out there. Sounds like you have several problems which may or may not be related.
You should not see any smoke up front when starting the engine so that indicates an probably exhaust leak for either a gasket, crack, or loose connection.
The rough idle after start... Does that happen each time you start the engine whether it's hot or cold or after 20-30 minutes of resting or only when sitting overnight?
Also what year is you Patriot and what engine do you have in it?
Lastly I can't find any FSM information out there for checking the fuel pressure. Obviously it will pump up to something around 35-45psi (I'm guessing) but then does the pressure stay there or immediately release to a low residual pressure. If there's no pressure in the fuel rail then I doubt very much could leak out of an injector. My YJ holds pressure for 30+ minutes but not sure about the Patriot.