<<Is a procedural approach position more challenging than a radar approach position as the controller needs to visualize the position of traffic without having access to a radar display?>>
Absoluutely not as they have Flight Progress Strip displays which carry all the information needed. Approach procedural controllers work mainly with vertical separation
<<Are all radar approach controllers also procedural rated - in case radar derived data suddenly disappears (such as when a screen breaks down, for example)? >>
I don't know the current rules, but when I did it, yes, they were separate validations. However, Approach radar controllers are more than capable of carrying on if there is a radar problem.