Filing federal tax returns for deceased parent. Any advice?

If the refund is subject to MERP, don't even bother.

Your DPOA ceased to be active when your mother died. You can't file a late, amended or final return for her. Only the executor of the estate can do that.

Yes, as an appointed representative, you can amend her previous returns. Again, if there is a refund due, you will need to file and sign form 1310. If there's no refund due, however, there would be little reason to amend. Only if the amended returns would affect carryovers to the 2012 and 2013 returns. Also, since she passed away in May, you may need to file a 2014 return for her. Depending on her income and withholding from Jan - May, of course.

My mother died in May 2014. I am now in the process of settling her estate. I too had some questions about amending my mother's previous tax returns due to some errors in how they were filed. Checked with lawyer who is assisting me and she told me that as her appointed authorized representative, I can. I mentioned O was also her DPOA. Doesn't matter, this action is being done after the fact.

Yes, you can file the original 2012 AND 2013 returns. You will need to include form 1310 Statement of Persona Claiming Refund Due a Deceased Taxpayer.
Check the appropriate box. Likely in your case it would be box B stating that you are a court-appointed or certified representative. You would attach your DPOA. Hopefully you also have a financial power of attorney. If so, attach that too. A copy of the death certificate should also be attached. You MUST sign this form as well as sign on the form 1040.

my mothers attorney was legally my mothers executor because according to him i was disqualified because i had a prior pill possession felony . i think he was flim flamming me on that but it didnt hurt my feelings because he still permitted me to handle all legal and estate division matters . i still filed my mothers final tax return with the help of my tax lady and we both chuckled about how considering there was a sizeable amount of taxes to be paid the irs wouldnt have cared if charlie manson signed the return on moms behalf .
im sure debralee is correct but i thought our case was pretty comical.

Only the executor/authorized representative can file an amended return on a deceased person.