Starting Problem

[98NB]

Hello to everyone I'm new on this club I bought corolla d4d 54 reg with 135k it had over heating issue so it fixed change water pump and timing kit it was leaking from heating matrix and pump as well now some time when engine is hot makes awkward noise while starting some one told me its miss fire so any one can suggest me what to do next and its also give black smoke while shift up friends says its normal with diesel and its my first diesel car

Thanks