Rotted sills are pretty commonplace and most of the rot that people see is often times draining behind the exterior cladding of the home and therefore not rotting structure. You need to take a closer look (i.e. remove some exterior cladding and inspect structure or remove the sill and take a look at the rough opening). While the rot may look significant, a majority of what is out there is non-structural and therefore does not require a full tear out. If you go full tear out, you absolutely should use a flanged/new construction window. Having asbestos siding certainly complicates matters a bit and you would be well advised to check code requirements as it pertains to that specific ACM (Asbestos containing material). There are more stringent requirements if the material is removed professionally (i.e. by a contractor) as compared to the homeowner (not all together dissimilar than the RRP fiasco).

You can do that in a pinch...we have done it on several jobs where what the customer wanted was not available in a replacement offering. The drawback to it is usually the frame is thicker so you loose more visible glass than you would with a true replacement, and a replacement is designed to fit into the frame of another window and be screwed in place, and the screw holes are pre drilled where that will not do any damage to the hardware of the window, drilling yourself you may hit a locking mechanism or other piece of hardware that would have to be replaced. You should be able to order the new construction window without nailing flanges as in many applications nailing flanges can not be used (ie concrete walls in some ICF houses)

If the framing is that badly charred, you'd be better served replacing the framing. Hiding the damage will only lead to other problems in the future. Since you have to do the window anyway, I'd do it all now. The nailing flange is located on the outside, usually hidden by some exterior trim or siding. Depending on the kind of siding you have, and the trim detail, it shouldn't be too hard to use a new construction window. But I would be concerned about leaving badly charred framing to support my home. You should have the wall inspected by a professional to determine the extent of damage before doing anything else.

Replacement windows are just that - the sashes ( using a double hung window as an example) are removed along with the jamb liners, leaving the frame of the old window, and a new window is inserted. Picture a frame within a frame A new construction (or full tear out as some call it) is where the entire window is removed right down to the studs of the house. A new construction window will have a flange that is called a nailing fin that is nailed directly to the sheathing/ studs from the exterior. All three of the manufactures you mentioned do make windows for both applications. In most cases a new construction window is not needed, unless of course there is great deal of integrity issues with the frame of the window you are replacing. Additionally, a full tear out job will generally yield more glass area. You mentioned three manufactures - two that make vinyl, and one that makes fiberglass (ultrex). Very difficult to rank from best to worst with these three, as they are all top producers. The difficult part of the ranking - you would need to determine if you want vinyl or fiberglass first. If you decide vinyl - you are in luck....you are right in the heart (Ohio) of a number of good manufactures.