If a mythic character has different powers granting him extra standard actions can this character use them all in one round? Is it possible to have several extra standard actions in one round or is not allowed to duplicate the same effect even from different powers?
E.g. I have 3 different powers and each of them allow me, spending one mythic point, an extra standard action, can I spend 3 points (maybe as 3 free actions) and get 1 standard action + 3 extra standard actions?
Yes, but take extra care with the action economy: if they're free actions, fine, go for it, but you could only do one that is a swift action per turn. Also, your GM may impose limits on your free actions, so ask beforehand: it would be completely reasonable for a GM to limit free action mythic point expenditure to only be done once per turn.
Likewise, a GM may choose to limit mythic point expenditure per turn, even without accounting for the action economy, so that even if you have one ability that lets you spend a mythic point as a free action, one as a swift action, and one as a move action, the GM may decide that you can only spend one point of mythic power per turn.
Mythic is a very powerful option, and requires a lot of GM oversight. Never assume that just because you've found the mythic source of OMGUberness he'll let you use it as written.
It depends on the specific ability and what kind of "action" is required to gain the standard action. The one I can think of off the top of my head is Amazing Initiative, which allows an extra Standard action, but only requires a Free action to use.