If I use a wood stove as a primary source for heating my house, is the wood

On the federal return, there is a tax credit (Form 5695) for the purchase and installation of "biomass" stoves and heaters. Biomass include wood. Please see the section under "Residential energy property costs" at the IRS 5695 Instructions.

This can give rise to a Nonbusiness energy property credit.

However, this credit is derived only from the purchase and installation of the Biomass heater, not the operation. So if I understand your question correctly, there is no tax benefit for the gas for the tools nor the chimney sweep.

Since I do not know what state you are in, I cannot say if there is a state benefit available to you.

your ordinary expense  of owning and maintaining your home is not deductible.

only property tax and mortgage interest.