If my total income is below 25,000 and I am 79 yrs old, do I still have to file Federal and State tax returns?

It depends on your filing status and the amount.  See below.  If your income includes self-employment income which exceeds $400, you would need to file a Schedule C and SE. 

As far as the state, every state's filing requirement is different. See here States for state's filing requirements.