Will wrapping the stove pipes with copper pipes increase wood stove efficiency?

In a woodstove, where the fire doesn't get very hot, you get a lot of unburnt gases. These are compounds that could burn but only at a higher temperature. Instead, they evaporate. As they travel up the chimney, the cool and condense. Over time it builds up. If you then burn a really hot fire, they can finally ignite, and your chimney burns. This can happen when you use a lot of pitchy softwood for a long time (Douglas Fir, for example) and then burn some really dry hardwood (e.g., maple).

If you do something clever to extract more heat from the chimney, you will get more condensed goop in your chimney, so be sure to clean it regularly.

Another way to deal with this problem is to always make a really hot fire. Then almost everything will burn, leaving very little goop in the chimney, and very little ash. That's going to be too much heat for your house, so you have to surround your fire with an enormous thermal mass. That will moderate the temperature. This is the principle behind a "Russian stove", among other names.

Not much. Copper is a good conductor of heat, but it wouldn't help much unless you made the actual stove pipe out of copper. Increasing the surface area of the stove pipe would, though, so if you want to solder copper fins onto it, that would help, and there's no need to worry about galvanic corrosion since the stove pipe is stainless steel.

That might end up being sorta ugly. If you really want to get a lot of heat out of this thing, look into getting (or making) a heat exchanger.

The gas leaving the stovepipe needs to have a certain temperature to be able to heat the chimney to actually create proper airflow by thermal venting.

The pipes you are linking to are actually meant to insulate the pipe, making it cooler on the outside, the gasses hotter, allowing the chimney to get hotter and generate more updraft, pulling more air into the stove, burning more wood, making more warmth.

Of course you can overdo this and have too much heat escaping as hot air. This is why the kind of stove, length of stovepipe and kind of chimney have an influence on the efficiency of the whole system.

If you have good draft, you might be able to extract some additional heat from the gas. If not, you may be able to profit from insulating the pipe to increase draft.

All this of course means you have to let air into the house from outside. If your house is new and well-built, it may be too tight to heat with wood. Try if your oven works better if you open a window slightly.

Also, dont mess with your stove without knowing what you do, or asking a professional. After all, you are dealing with a column of flame passing through your house.

Air is very bad at transferring heat. This is why all modern insulation is based on air bubbles. You can only use the heat that is created by the fire, no more -no less. You cannot use copper or anything else to manufacture more heat than that provided by the fire. As mentioned elsewhere you need a hot chimney to help the hot exhaust gasses escape.

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