Window insulation film.
This window kit is clear plastic sheeting. You attach it with double sticky tape along all edges. When I did this the last step was to blow hot air on it with a hair dryer which got rid of wrinkles. 3M makes a kit. The plastic must be something like shrink wrap but I dont know if that ...
You have a few options:
Place the casing over the drywall and jamb as usual, and let it tilt a bit due to the 1/8in difference.
When you apply the caulking to the seams, the difference will not be noticeable.
The bevel joints at the jamb corners will be slightly dipped, and you can minimize the visual distraction by applying some drywall compound and ...
You need to find the source of the leak and stop it. I would start looking at the top of the window frame . Likely it is entering at the interface between the window frame and a wall ( on the exterior surface.)
So if I understood correctly the water enters between the sill and the master frame. Why not seal it with silicon and this tool (don't know the word in english)
Use plumber silicon or other silicon used for moist environments. Place the silicon generously and "detract" it with the tool shown. This should seal it thoroughly.
The seal between the two panes of glass has failed, allowing water vapor to diffuse into that space. When temperatures are right the vapor condenses as a haze/mist/fog on the colder piece of glass.
You can't "fix" the glass unit DIY, but replacement is within the realm of DIY (assuming there isn't a warranty that will take care of this for you!). ...
"Hazing" within a dual-glazed window or door is a symptom of failure in the sealing that's supposed to maintain unchanged whatever (air, other gas, vacuum) is within the space between the two panes of glass.
Windows and sliding doors in my house were replaced with dual-glazed panels in 2008; several panels have recently developed a similar ...
@FreeMan had the right idea, the tabs were the key!
The tabs had to be pulled and rotated clockwise. Mine were stuck pretty hard, but after pulling it with all my weight it finally rotated.
Here are the pictures after I took it off.
I agree that the source is likely condensation. I also agree that opening the windows when possible and wiping off the window will both likely help. A fan may help as well (after the mold and its roots are removed... you don't want to spread the spores).
If you don't mind the aesthetic change, you may want to cover those sills with something non-permeable ...