Now I make my new HTML template. And there are differences between browsers from PSD file. They are tiny, but they are there. Is it strong requirement from Themeforest to design templates pixel perfecty?
No, this is not the reason for the deviation, if it is a deviation that can not be seen, pixel perfect layout requires, as it seems to me, much more effort than usual and takes more time. Although, if you want everything to be perfect, you can worry about it.
It needs to be as good as it can be, but I would focus on originalty, attention to detail and error free code
in case of spacing and allgnment I would like to say yes should pixel perfect as like section to section padding should be consistent. But it is not required to be 100% same as PSD. Just need to be error and issues free consistent design.