The interior to the house is completely tarnished, so cabinets, walls, ceilings, stairs, flooring, paint, appliances, etc. are all trashed.

I always replace toilets, shut off valves, water fixtures, add frostproof water spigots with additional isolation valves for winterizing, switches, light fixtures, Add ceiling fans to every bedroom, GFCI outlets, regular outlets, smoke detectors with 10-year or hard-wired-in, use a quality one coat semi-gloss paint, basic white washer/dryer and Exterior door locks with touchpads (key free). 

 Is a super insulated false ceiling possible?

It's not as bad as it initially was but my guess is previous tenants were in there smoking for 20+ years and maybe not just cigarettes, plus there was dog urine as well....We have replaced drywall in some areas, skimcoated and painted, new textured ceilings, pulled out carpet, replaced floorboards, put down new lion boards and new LVP flooring, new paint, all new appliances.

Because my rents will remain at, or below market (even with the increases), and because my existing tenants are highly satisfied, I'm hopeful that the rent increases won't cause any tenant turnover...time will tell...One problem I may encounter is that rents in the broader market are currently pretty flat, so even though I'm currently below market, there may be a ceiling to how far I can increase.

Every time it rains the ceiling leaks inside as well.

Installed LVP flooring throughout, all new appliances, painted, installed crown molding, changed bathroom vanities, fenced in the back yard, installed new ceiling fans and lighting throughout, changed lower kitchen cabinets and countertop, painted upper cabinets, installed two new windows in the house, changed HVAC, and furnished it.

We changed the flooring to LVP throughout, painted, added crown molding, installed new lighting and ceiling fans throughout, did light cosmetic upgrades to the bathrooms, fenced in the backyard, removed dead tree from front yard, and re-graveled the driveway.

I became very proficient in installing ceiling fans and light fixtures as well as doing minor improvements such as updating the bathroom vanity and changing out the counter and sink faucet.

You're likely going to have a much higher floor for your money, but likely a lower ceiling.