I have been in US since 2005 and this is the first year I have to fill out resident alien form. I have been working voluntarily and haven't been getting paid for it. Do I still have to document that somehow or have evidence or some kind of form from the employer or not?

If you did not have any income, you do not need to file the tax return.

I do have a 1099 MISC form though from a different employer for a one time thing I helped out with.

If you have more than $400 from self-employment (from the 1099-MISC), you need to file a return. You won't owe income tax, but self-employment tax.
Otherwise you only need to file a return if your income is more than the personal exemption plus standard deduction.

I have a couple more questions:

1) I was told it can be considered OTHER INCOME and be put on line 21 if it is a sporadic activity or a hobby. This is apparently an exception. Is that true?

2) I have received form 1042-S from University where I had a full scholarship.
All the info that is on it:
Box 1: Income code 15
Box 2: Gross Income : 6609.03
Box 5: Tax rate 14.00
Box 7: Federal tax withheld 925.27

My questions is: do I have to put any of that information on form 1040? If yes, then where (what lines)?