From this description, the metal "chimney" going through the basement wall (to where on the outside?)would be a real safety hazard not to mention a violation of fire and building codes. Your insurance company would, in all likelihood, never approve of such a setup, either.

Your local fire department should be able to advise you about this arrangement, but even though many people do have basement wood stoves it's never a very effective way of warming the house even with grates cut into the basement ceiling.

The 'chimney' doesn't go through the wall... it is type #2 diagram on the link below. I just don't know the proper terminology

Here is a link that might be useful: wood stove setup

If the chimney portion of the set up - the part in type #2 which extends vertically up the outside of the house - is a Class A solid fuel metal chimney, then it may well be fine for use. Certainly have it checked and cleaned if needed before firing up the stove, though.

If you want to check the interior condition of the chimney yourself, you'll have to detatch the stove pipe at the junction with the chimney and use a mirror to look up inside. A certified chimney sweep would likely have more sophisticated equipment to assess the chimney's condition. Exterior chimneys often become clogged with creosote, especially in cold climates.

The usual problems of basement wood stoves are: poor draft, inconvenient place for feeding with wood, poor circulation of warm air. Much depends on the house setup, insulation, etc. Another reason for seeking the advice of your fire department, a sweep, etc.

I'm not planning on using the stove as the primary source of heat, but rather to supplement the electric heat occasionally. Thanks for the advice mainegrower, I will contact a sweep to have it checked out.