Cracks in the ceiling corner & nail pops

Am getting a 1920’s home renovated. Location is Southern California. This is not a DIY post requesting help but one asking for advice on how to proceed and have contractors do the right work for the house’s specific case. Some questions: Ceiling: It has plaster ceilings. Some of the plaster has broken off from what I assume was previous water damage. It seems rather than replaster, it would just be easier to hang drywall. A contractor said the loose and all existing plaster will be all removed but the lathe will stay and ½ drywall can be hanged. I asked why not ¼ given weight considerations and his response was the ceiling might look wavy with the thinner drywall. Also, the lathe can stay unless planning to put up insulation (as the house has none). Even if I do not want insulation installed, should the lathe be removed anyway? He said one reason was that it gives the ceiling more strength to let it stay in place. What do you think? Thanks in advance!

Hello and BIG Thanks in advance DIY guy here tackling a man made stone veneer wall / backsplash in the kitchen. I mixed the Sakrete Veneer Thinset to specs 6 Quarts of water to 80 lb bag. Seemed kinda dry but also understood that its probably suppose to be a bit thicker to handle the weight of the stone. Anyway, backbuttered the stones with 1/2" or so of the mortar and created a 'vacuum' channel down the center and pressed against a water misted wall. A really hard wiggly push squeezed out a bit of mortar from the sides....a bit. Anyway waited to the bottom level to set a bit then worked up... The Problem...or maybe the problem. When I was pushing some of the higher stones it would apparently disturb/vibrate the backer board to the point where a title or two below would POP off That was POP off....not slide or shift. The entire stone complete with all the mortar would pop off. Is this typical until the grout is piped in? I did wait a couple hours hoping for a bit of curing....and gently with the tip of my finger pried a stone and it popped off as well. More time to cure? Grout? Or maybe mortar too dry? Before I get too far I want to make sure I get this done right so I dont have a MAJOR problem down the road. ANY help is GREATLY appreciated! JPICC