What you have is commonly refer to plastic laminates, the lamination process require high pressure and heat so its pretty hard to redo it on your own. If you don't want to replace the whole unit, you can replace just the doors and screw a new sheet of 1/2 finished wood (or new plastic laminate)...
depending on the size and cross section of your duct, you might be able to find a 90 degree elbow at home depot that'll do what you want. Just remember that every turn you make reduce air speed to that outlet so you don't want to add too much length or bends to a duct.
Didn't think that this could be DIY due to the equipment required as Kok328 said. If you have all those equipment then you'll probably already know how to do it.
Don't think its a good idea, it'll slow the air speed way down since its too far from the fan. Its like trying to breath through a mask, you'll be huffing and puffing but only getting half of the air. I have done a "flush" of the HVAC system before but only on large commercial building with...
If you water proof the inside face of our foundation wall, all that mean's that your wall is now gonna be soak and underwater and will deteriorate even faster. You need to excavate the outside and waterproof properly. Either do the job properly or you'll be forced to do it properly latter on at...
I know they make chemical accelerator for curing concrete in cold weather, not sure if they have the same thing for mortar but you can check. Not a recommended practice though since the strength of the cured concrete is lower.
We pump concrete through a hose all the time, that's how all the high rises are build in the city, a giant crane truck with a long hose and strong pump to get it up 40 stories.
Restricted workspace do make it harder and drive the cost up a bit.
Sounds like it might be the frost thaw cycle causing your basing concrete floor to heave, in which case it is coming up. Properly design spread footing shouldn't be sinking faster then the rest of the basement floor. I would try getting a sump pump first.
Sounds like hydrostatic pressure (pressure from water in the soil) might be the cause since you are on a hill and get a lot of surface water. This also often cause the lower course of your CMU wall to bulge like it is shown in your pics since the water would collect around the footing. A missing...