Q: Black smoke, intermittent starting, overflowing coolant with cap off

-2004 Jeep Grand Cherokee Laredo 4.7L V8. 134k miles

Codes: -P0420 (Catalyst system efficiency below threshold bank 1) -P0302 (Cylinder 2 misfire detected)

-Car doesn't usually start on first try. It'll either crank for 5-6 seconds and start weakly, or it'll just keep cranking. If it doesn't start after 5-6 seconds (but it does crank), then turning the power off and trying again starts it 90% of the time immediately (normal start). May or may not be unrelated - the battery is unlabled and undersized. It only takes up about 60% of the space of the battery tray. Black smoke from exhaust when accelerating (around 40%+ throttle) Strong gas smell from exhaust smoke at idle

-Not sure if this means a bad head gasket, but with the radiator cap off, revving the car to 1.5k makes the coolant overflow. The coolant level doesn't move at idle. Here is a quick gif (the level seems high because this was the second time it was revved. It sits a bit lower at idle): http://i.imgur.com/1Mx2B1U.gifv

My car has 134000 miles.
My car has an automatic transmission.