The reliable way to hire a tradesperson

Does the lath and plaster need to be removed or can a stud frame and plaster boarding cover the existing ceiling

Carpenter is fitting new internal hollow doors, old plain doors had three hinges, he is only using two hinges on new doors, said it should be ok? My question is what works are required to patch up the middle hinges and space around new hinges which are smaller than the previous ones, who will fill the spacing carpenter or decorator?

double door , the one door won’t close properly and seems to have dropped leaving a gap at the top