The earth underground is 50-55 degrees F for much of the USA. Carpet and pad are very good insulators. This is important if you use the basement in the wintertime. Concrete/tile/stone are very poor insulators and the floor will feel cold. Of course, this is not an issue if you have radiant floor heating. Engineered wood or laminate are somewhere in-between for insulating value but not nearly as good as carpet and pad. I think replaceable carpet tiles with attached pad would be the ideal basement floor. I have never used this type of product. I'm not a huge carpet fan, but it works well in our basement with kids. We have a 1/2" nylon pile and standard pad that is soft and easy to clean in a darker color to hide stains. Ours is a bi-level, so we do have regular double hung windows for decent light and the walls are a light color. Insurance will take care of the backup or water heater flood or sump pump failure if it ever happens. Thankfully, our sewer line has no trees between our house and the main. The water heater is also new. The sump pump is the only real risk. I will be installing a battery backup in the near future as the power does go out here fairly often during big thunderstorms when it rains heavily. I have been home on two occasions when I had to bail the sump pump well, very LUCKY!

The DriCore R+ is closed cell STYROFOAM with OSB mounted on top. I can tell you that it is the vapour barrier system that DriCore produces for situations like yours. Your description makes it sound like the styrofoam was a jerryrigged system that mimics the DriCore R+ system. If the screws PIERCED the styrofoam and PIERCED the VAPOUR barrier, you essentially had a bunch of holes punched in the water-proofing system. The holes = water intrusion. And NO....LVT products do NOT LIKE underpad. That's why I'm suggesting going with a system that ADDS an R value. DMX has very little R-value. It is about the same as plywood. And just in case I misunderstood your post and there were NO HOLES IN THE VAPOUR BARRIER on the slab, then you have a MUCH BIGGER ISSUE than you anticipate. The stains on the DRYWALL is the big red flag here. And if you want an underpad, the DMX REQUIRES PLYWOOD to be placed over top! Yep. It says it in the very fine print of the INSTALLATION instructions. And to put the plywood on top....you need to SCREW IT DOWN onto the concrete!!! You need tapcons. And you need to the right drill bit, etc. And the DMX is HARD to "shim". You still need to get this floor flat enough for the LVT. Whew. DriCore R+ is SOOOOOOOO much more appropriate. The stains on the drywall concern me.

we used LVT as our walkout basement flooring. Finished on site hardwood everywhere else. I like that the LVT is everywhere in the basement including the bathroom floor. Lots of wet, sandy people coming into basement from lake. So far, so good. we used cork in our last house in the basement and even though it was warm, soft and luxurious..it didnt hold up. I think the LVT will hold up better.

The gas hot water seems to have a power vent. I will defer to the hot water heater experts to determine if this arrangement is cause of concern for back drafting. It is hard to tell from the photo, but is the gas line feeding the furnace and hot water heater 1/2 inch in diameter. That would seem undersized for a 100K BTU furnace and a 40K or 50K BTU hot water heater. Maybe the original intention was to install the 45K furnace but when it was changed to a 100K no one considered the size of the gas supply line. I agree using a lawyer is the last resort. The builder may be trying to run out the clock on the one year warranty. You have consider it if he has nothing for 7 months and you have health concerns. Are they any inspection stickers or records that indicate an code official approved anything?