I recently had a crown put on my right lower molar. The tooth is now sensitive to heat and cold, my TMJ is bothering me, and it feels like i'm biting down on rock. Can a crown be removed and, if so, will there be enough of a tooth to be able to chew?

If the crown is removed, the tooth has to be crowned again using the same crown or a new crown. The question is why the tooth is sensitive and why when biting on it it feels like a rock.
You need to have the crown checked by your dentist, there could be a possiblity that the crown is high and needs djustment (more likely), or the nerve inside the tooth is stressed and the tooth might need a root canal treatment (less likely).

Its normal, our body takes time to get use to any foreign material. you will start feeling normal in a few day and if the problem persists then it means that the crown is high, then you will need to get it adjusted by your dentist. He will grind the parallel tooth.

Hope this will help.
Kind Regards,
Pete,
throgsneckdental.com