So, when pyat or simmilar effects trigger and I play Red Venageance, wich makes the targeted player be the one suffering the claim… What is the result? Do I select a char from the pyat controller and kill it? Does he chose a char to kill? Does the normal claim take effect? Does it depend on the order of responses (not in case of pyat, since it´s a passive, but in other cases).

Pyat Pree's controller chooses the character (controlled by Red Vengeance's target), because.Pyat Pree's effect changes the whole claim, including how many targets and who chooses targets. Red Vengeance doesn't interact with Pyat Pree's text, it only changes which player suffers claim.