Please help 1.8 non turbo takes ages to start and lumpy idle

Hi everyone I hope you are all well. I bought My Audi A4 B5 1.8 non turbo with engine code AVV about 3 weeks ago. When i went to look at it i knew something was wrong and I should have walked away but the guy kept talking to me diverting my attention away to a tear in the seat, I have autism so I became very confused and bought it anyway for 550 pounds which was all the money I had in the world. When I got home which was only a 5min drive away I immediately regretted buying the car and knew i made a big mistake. I turned the engine off and tried to start again and it did eventually but it took a long time and idled with a misfire or several. It starts easier when warm but from cold it takes a good 60 seconds of turning the key before it stutters into life. At first it sounds like its only running on 1 or 2 cylinders but then after about 5 seconds as revs increase the others do fire but still with a lumpy idle. I tried to take it back and explained my situation but all the guy said was Sorry sold. I have had a friend look at it and attempt to fix it, he replaced the inlet manifold gasket as we saw smoke rising from that area and after removing the manifold he also found a big hole in the crankcase breather hose which has been replaced, but the car still takes a very long time to start from cold and still idles rough? Any advice will be very much appreciated im hoping it can be repaired cheaply by my friend as I don't have alot of money so I need some pointers as to what it could be. Also my friend does not think it is the head gasket that's failed as there is no smoke from exhaust just white smoke (water vapour) from a cold start.

Thanks again

Hi Andy Yes check engine light is on, I have no idea when it last had a service though. My friend did a fault code scan before the manifold gasket and breather pipe were replaced.

Ok thanks i will get some new plugs and a fuel filter, i hope it isn't the coil pack though, sounds expensive!

Is the temp sensor easy to access? As probably can do that one myself

I went for a short drive the first one since having the manifold gasket and breather hose changed... About 5 mins in the car started making a terrible noise, it sounds like a diesel is the best way I can describe it, not even just when accelerating it sounds like it on idle too.