I was dropped from my health insurance policy and now owe penalty taxes because I wasn't covered the entire year. Is there a hardship exemption, or a way to avoid penalties for not having coverage the whole year?

[SDBaldie]

Yes, you qualify for the hardship exemption. The process to get this exemption does take a little time, and so I recommend that you file an extension while you go through the process. 

Select that exemption in the Health Insurance section, and click on the link to take you the healthcare.gov website. Fill out the forms, provide the documents, and submit the paperwork. In about 2 weeks time the gov't will send you an ECN (a number), which you will enter in your taxes, and which will waive some or all of the penalty. 

Hope this helps!