Chimney and fireplace removal

It will be next to impossible without doing major major structural work. The house was built around the fireplace, and I would assume they are holding each other up. It would be much cheaper to have the chimney capped and fireplace blocked. You could possibly even frame a wall or something over the fireplace once it's blocked if you choose to.

Actually most of the fire place that was built inside are not connected with the structure of the house. Normally joists/rafters will go around that brick junk and it is very straight forward to remove them. Any demolition/masonry companies will do that for you. It will be 1 or 2 days job depending on the size of your chimney. The price will range from 3k-6k. Please make sure that you chose good contractors with references, insurances, etc.
You should probably pay more though on how to close the opening as well as to deal with dust when they remove the chimney. It will be dust like hell.
However, in some rare cases you will find that some beam/joist rest on that but it will be an issue later on so you should fix it any way.

I read that a chimney in an internal space is better than an unheated exterior location. Reduction in cold drafts with this setup. I found a really good write-up on this on the Droulet website site explaining the physics of it.