Do Roman Catholics believe Saints are omnipresent?

I understand that officially speaking when Catholics pray to saints, they are not supposed to really pray TO that saint, but rather are asking that saint to pray for them as you would ask any living friend to pray for you. The Bible does indeed say we are surrounded by a great cloud of witnesses, but How is a particular saint supposed to hear me asking them to pray for me while John in England is asking the same thing. Are saints supposed to be omnipresent, or are you just rolling the dice that they are paying attention to you at that moment? Is there any official doctrine explaining this? Are all the saints watching all the believers all the time, or what? Are they in many but not all places? Bonus question, if a none-catholic christian asks them to pray for them do they hear that?