Car running rough and idleing at 2000rpm

My battery went flat and I live on a hill previosly ive let the car roll down the hill and bump started it this way. I tried this method again yesterday however instead of engaging in reverse gear I believe I had it in first gear. When attemptin to bump start this way and when I lifted the clutch power came to the car as I saw the dash lights bright up however I heard a bang and smoke seeping from the bonnet.

I have then jump started with jump leads, car has started fine however very rough, clutch and gearbox feel rough and not like how it was previously, when idle after slowing down from speed and coming to a stop car idles at 2000 rpm. I have opened the bonnet and I hear a sound like the engine is sucking in air but cannot locate where from. Seems like a pipe is disconnected or something.

all the functions in the car are fine its just that it sound rough at idle once driven it drives rough and when coming to a stop it idles high.

Please help me diagnose