How to install a window air conditioner and still allow the window to be opened

Since it sounds like it might be difficult for you to get to a lumberyard to build your own solution, you might be better off using a pre-made product. AC-Safe, makes Universal Air Conditioner Supports that might be useful in your situation.

The system requires you to screw the platform into the window sill (which may or may not be possible in your situation), then simply rests against the outside of the building to support the A\C unit.

I've also seen brackets that mount to the bottom of A\C unit itself, and offer support against the outside of the building (but I was unable to find an example online. I think Thermwell makes them).

Given how low you're keeping the apartment temperature, and given that the ambient temperature is relatively warm, I think you can probably get away with leaving it in place. You'll lose some heat, but nowhere near as much as you would if the differential between inside and outside was greater.

Digressions:

I've seen some weird-and-sometimes-wonderful approaches to AC mounting. I've generally used smaller units that could get by without external brackets, but I've seen one (in NYC) which used a steel square-bar to bridge the opening and carry the weight rather than letting it rest against the upper sash.

The one time I had an AC which really was too heavy to lift, it did have outside brackets built into its case (rather than permanently installed to the wall). The proper solution was actually to mount the case by itself and then slide the guts into it, rather than trying to manhandle the whole thing at once. When dismounted, I kept the mechanism on a rolling cart that was almost at the right height, so I could slide it from cart to case and back without ever having to lift the full weight.