Just bought 2005 Honda CR-V, i paid 3300$.
1) In idle when the AC is on the car is idling the rough it's sounds a bit like a diesel... when the AC is off it's smooth again.
2) I suspect the engine is running rich, I wiped the inside of the exhaust with my finger and it was musty and thick, and I think the fuel consumption is high (I did it run accurate test yet) when I'm starting the car it takes three or four spikes, what could be the problem? After I bought it I went two bottles of Chevron high mileage fuel system cleaner.
AC compressor is going out.
One question per post please.
Not knowing what kind of maintenance it's had, I'd start by checking and probably replacing 3 cheap and easy things that could cause richness (or oil burning which may be causing your blackened tailpipe). 1. Plugs 2. Air filter 3. PCV valve.
It would probably be a good idea to do Scotty's Tune-up in a Can, too:
https://www.youtube.com/watch?v=NWCKvU2FmDc