Tax Year 2016: Both parents died in 2016. Can i file a joint return for them still? Do I also need to file a return for the estate even though it didn't have income?

[KarenL2]

I'm sorry for your loss.  Yes, a Married Filing Joint return can be filed for them.  Also, if there is no income for the estate, then you don't need to file an estate tax return.  https://www.irs.gov/instructions/i1041/ch01.html#d0e340

"The fiduciary (or one of the joint fiduciaries) must file Form 1041 for a domestic estate that has:

1. Gross income for the tax year of $600 or more, or

2. A beneficiary who is a nonresident alien.

An estate is a domestic estate if it isn't a foreign estate. A foreign estate is one the income of which is from sources outside the United States that isn't effectively connected with the conduct of a U.S. trade or business and isn't includible in gross income. If you are the fiduciary of a foreign estate, file Form 1040NR, U.S. Nonresident Alien Income Tax Return, instead of Form 1041. "