Replace the glass plate of a ceramic stove with heating coils: can I use any heat-resistent glass

I will assume this wood stove has a proper air jacket from which heated air can be drawn? The possibility of dangerous gases infiltrating into this jacket is a valid concern and entirely dependent on the integrity of the firebox. This can only be done by careful inspection and possibly some sort of pressure test. In theory, this can be just as safe as any other fuel burning furnace.

The purpose of piping the stove's heated output air to the furnace return air is that the furnace is then fed pre-heated air. This minimizes the amount of energy the furnace must use to raise it to the proper distribution temperature. It doesn't make sense to apply the wood heated air to the furnace circulating air unless the furnace's output temperature was deliberately reduced, relying on the wood heat to make up the difference. This would be very difficult to properly regulate since thermostatic control of a wood burning appliance is marginal at best unless you are burning wood pellets.

Whether the pre-heated air from the wood stove is bad for the furnace would depend on just how hot this air is. This is highly variable depending on air flow, fuel wood type and loading, as well as combustion air or damper volume. With adequate air jacket flow and typical wood stove firing practice, I don't see this being a problem for the furnace. But there's a lot of variables. It would be easy to misfire the stove and reach damaging temperatures.

Some sort of damper bypass system would be ideal, but the controls needed would be complicated to ensure adequate heat was delivered regardless of the stove's firing rate. Even then, it will require careful monitoring. It'll always be possible to over fire the stove during low heat demand conditions, wasting fuel.

In my area it is common in rental units to install panel doors in lieu of mirrored doors. We buy the mirrored door track, frame, roller, and hardware kits but with no mirrors. They call it a "knock-down" kit. We then cut wood or composite panels to fit where the glass would go. The manufacturer even gave us a table with net mirror glass dimensions, to use when sizing the wood panels. Check with a local high-volume window and door shop. You might even be able to get the kits from a "big-box" hardware store but I prefer to work with the guys at the sash and door shop for the personal service and expertise.

You might even be able to use your old frame and hardware, measure carefully first, then take apart the frames (they are screwed together) and cut wood panels to fit.