Using a window as a dry-erase surface

There doesn't appear to be too much holding them in at the best of times. Unless you want to replace the entire window you should look at getting the top and bottom sills (or whatever they're called where you are) straight. From your description I would say that there is a pretty significant difference in the opening when measured at the edges and the middle. That shouldn't be the case at all.

Remove the trim from at least the top and bottom of the window frame and shim the top and bottom as required until you have a nice even distance all the way across. Then replace the trim and touch up the paintwork as required.

This is not meant to be a complete answer, but might help with your understanding of it. My understanding of the physics of windows is as follows -

Nearly all radiation (visible, UV, infrared, every other type too) that travels from outside the house into the house and is absorbed (not reflected back out again) is converted into heat. I would expect that exceptions (such as the energy from UV light causing a chemical change, such as when it fades your couch, or waves that induce a current in a conductor) are relatively negligible.

This means any radiation that can be reflected from the window to prevent it entering the house reduces the heat load. Also, if the radiation is absorbed into the window glass (eg through tinting it), then some of the heat from the window glass will be lost to the outside (through both conductance/convection and some radiated heat) which is an additional benefit.

A heated window pane would like lose more heat to the outside than the inside because the wind would help keep the temperature difference between the glass and the adjacent outside air larger than the temperature difference between the glass and the inside air.