A properly designed wood burning kiln could reach cone 14. Firing to cone 6 would be no problem, however if that's the temp you plan to fire to then you would want a kiln that produces very little ash, otherwise you'll have dry ash on your pots. The other option would be to fire your pots in saggars to protect them from the ash. To get the effects that you see in most wood fired pottery (ash glaze), you need to fire to at least cone 9 for the ash to melt well.
It depends on the design and the type of brick used, but yes. I don’t know of a wood fired kiln that wasn’t purpose built. Most of them are designed go much higher than cone 6.