Only if they are in two different clauses, since the form of to be with I is "am".
Examples:
"I can see that it is raining outside."
"I am the one who is responsible."
(unless we use the facile "The letter I is after the letter H.")
They are both happy. NOT They is both happy.
"They both have great humor" is a sentence.
It is both a question AND a sentence.
both sides
Yes
The term for a word or sentence that reads the same in both directions is "palindrome."
It is a sentence because it contains both a subject and a verb.
Hammer and nails are both the subject of that sentence.
we both went outside
Both of the tests were easy, to me.
both and
Yes both words have same meaning!