Most seeds will be killed off in a compost pile if done right. The standard mixture is 50-50. That is 50 percent brown material such as leaves, paper, soil, straw etc. The 50 percent green material such as manure, grass, and kitchen waste is what provides the heat needed as the green material starts to decompose. The ashes from the wood stove can go right in the garden or mix into the compost itself. The burn pile only if it is clean material that has been burned, as I agree there are usually too many chemicals in the ash to use in a garden. The pile of compost should be turned weekly to keep it mixed and working. I have a very large compost pile but my problem is I never have enough green material, even though I bag all my grass and put it in the pile. The manure is hard to come by as anyone who has it wants to sell it.