The unit is a mixed bag. On the one hand, the plumbing leak could be repaired and the unit might work great. Otoh, the service engineers may have diagnosed the issue correctly and the blockage would cause the plumbing to leak again. I would definitely look into warranty replacement, since the unit is fairly new and the repairmen have built you a solid case for a manufacturing defect.

The LCD panel is bleeding to death. End of life for it is past, you're on borrowed time now. Time for a new LCD screen or a new TV.

As far as the battery with an external charger, it depends on the battery connection. If you have the old school flat contacts on the battery, a universal charger will work. I bought one off of eBay that works better than the one I found at batteries plus. Model YBY-001-018. I had the same problem with a galaxy j7 and ended up replacing the charger port / headphone / vibrator cable assembly. If Samsung had put the charge port on a board, I may have been able to replace just the charge port. Nope, all one piece.

Time for a service call. If the compressor runs but no cooking, there's either a leak or a clog in the refrigerant plumbing. Impossible to tell without breaching the system, as current draw is small .

I would replace the backlight LED strip first. Since your tv is edge lit, it's not a big deal to replace. Not overly expensive either. It's impossible to tell which one is bad (led driver or LED light strip) without some trouble shooting and testing being done first. If it's the strip, the unit will be easily tested with a known good strip connected. Do this before the existing one is swapped. If the led driver is bad, a known good strip will still flash. Then you get to do board level repair or just buy a new board.

Broken screen due to internal injury. Start saving money for another tv.

Window AC units typically have standing water in the outdoor half to improve the energy efficiency of the unit. The outdoor fan has a “slinger ring" on it that picks up the standing water and wets the outdoor radiator. This lowers the temperature of the outdoor radiator through “wet bulb" evaporation, and the hotter it gets outdoors the more it helps. The easiest way to get rid of the moldy funky odor is to keep the unit sanitized. Clean the air filter and use a bathroom sanitizer type of cleaner on the indoor radiator. There are two main types of cleaner sanitizers: oxidizing agents (chlorine bleach, oxy peroxide, toilet bowl cleaner acid) and alkaline agents (ammonia, scrubbing bubbles, windex). Pick one and use it on the indoor side while the unit is shut off. Let the agent penetrate and do it's job for a bit. Spray some rinse water and let that follow the cleaner outdoors. Put the unit back to work and the outdoor side will usually take care of itself.

Take the car back to the mechanic and ask about the shaking issue.

Sounds like a fuel system problem. My favorite lawnmower cleaner is e85. Go get a half gallon of it and some colored 2 cycle oil. Replace fuel system fuel with e85 mix and remove carb bowl drain screw or entire bowl. Catch escaping fuel and clean up the bowl if totally removed. Put carb back together when fuel changes color. Drain remaining e85 and use for cleaner or in your flex fuel vehicle.

You're not an electric wizard. Please don't die trying to fix this. 230 volts is powerful and lethal. Sounds as if you procured a general purpose replacement for the dead motor and now it's not going back together correctly. Look up schematic diagrams and connect the dots. If your new motor isn't the same as the old one, it can be made to work with labor and materials. If you mess around too much something will die. Then you will spend more money on it or get shocked or both. Find a schematic reader.