So radiation does give you powers ?

Well.. radiations selects for powers.

Nah, just filters out those that are weaker/less resistant.

Everyone has radiation resistance. Our DNAs repair mechanisms protect us from DNA errors from all sorts of sources.

A region where high radiation exposure becomes daily life simply makes the this trait the dominant one for animals to live long enough to procreate, meaning the ones with the best mechanisms will survive, the others die.