Are there any rules (unofficial of course, i'm aware that there is no formal regulation for this) for voting for end ?
In 2vs2 game with one of the opponent booted in first turn [before picks] I always agree for it. One turn later I usually also agree(however reluctantly because of few situation when players fleed after don't getting primary picks).
But now i have been asked fot voting to end in turn 4, when one of opponent surrendered after getting seriously hurted. We've refused as it was clearly admitting defeat by one of them. Do you think it was ok or should we agree ?

Yes that's quite alright, exactly how i feel.
I hate when one person asks to vote to end after their teammate left cause they were smashed. The only times to vote to end is when either someone is booted while the game is still close or if someone has to leave and the game is close, otherwise you deserve the win.

I agree with you about everything except theres a couple additional things that i think. first, obviously, its pointless to vote to end in a big team game like 8v8 or 10v10. I also think that voting to end makes sense when the game has relatively small teams and the game is currently at a relative stalemate. Often I find that a team does very badly, one person gets booted and then the other teammates ask to vote. That doesn't make any sense.

Voting to end should be done in stalemates or in the first few turns of the game when a boot happens or a player mistakenly had to go already.