Winterizing?

You can buy kits, very cheap. In it there is a roll of clear tape. That goes around the window and the plastic sticks to it. The directions are easy to follow.

your local hardware store have lots of plastic windows available. you use a hair dryer, like plastic wrap and heat it to stay on the window frame. check with your hardware store for tips.

use some double sided tape all around the frame and just stick the plastic to it.

Yes you can. Use double face tape for the plastic or bubble wrap. There is also this product

On the window behind this sofa we installed plastic on a kind of permanent basis. Since we have two doors in the room to the outside we figured we did not have to open this window and the big one is stationary. Since these are antique wooden windows double sash with the wooden stops,, we just removed the stops, placed and probably stapled the plastic in place and replaced the stops. The plastic does not show at all. For windows that don't show at all, you could buy sheets at the big box stores that can be cut to fit (can't think right now what the material is called but it is lightweight and insulating. . . but also solid) You could also make frames for the plastic sort of like you would make frames for screening. Depends on your skill level, what tools you have etc. If it is strictly for preserving warmth in the room I have found that pinning cheap fleece blankets inside my curtains helps a lot. And it also gives a nice weight to the curtains.