Do Roman Catholics believe Saints are omnipresent?

Question

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?

Answer 1

Are saints supposed to be omnipresent, or are you just rolling the dice that they are paying attention to you at that moment?

No they are not omnipresent (or omniscient for that matter), only God is. But they can hear our prayers by the power of God. Since we believe they are in heaven where they dwell in God, it is not strange that they can hear multiple 'messages' at the same time. Heaven is not present in "earth time." Heaven is outside of earth time, in-fact there is no time in heaven. Eternal now is that all is there. The saints live in the power and energy of the Divinity; So, They hear us through God.

The saints are aware of our prayers is that, because they have the beatific vision of God, they see in God all of the knowledge they need, all of the knowledge that is relevant to them, and so they see our prayers to them. On the standard account is thus by the omniscience of God that they become aware of our prayers, though they themselves are never omniscient and never take in the full scope of God’s knowledge, only those parts that are relevant to them.^{James Akin}

We do not expect them to be listening to us at "that moment", because they are not "in that moment", but they are out of it.

They hear us through God, more specifically Holy Spirit. In the Holy Spirit, we have communication with all the Saints, because of this, it is the Holy Spirit that unites us, spiritually. Bible says that it is the Holy Spirit who prays on our behalf.^{Romans 8:26} So it not not a big deal for God to make this happen.

Bonus question, if a non-catholic Christian asks them to pray for them do they hear that?

Yes they do.

Answer 2

Short answer: No.

Long answer: Those who are beatified and those who have been canonized have physical bodies which are (mostly) on earth (Mary, Enoch, Elijah, and Moses being exceptions). They are also in heaven in spirit. This means that they are in a very specific spot (even though heaven is quite large).

God, on the other hand, is literally everywhere (cf. Psalm 139).

---

I think it might be a good idea to point out that the question seems to be conflating omnipotence, omniscience, and omnipresence. Addressing omniscience and omnipresence:

Omniscience:
Saints are not all-knowing. While the Spirit perfects the communion of the Saints, it does not make it equal to God himself. A podcast I once listened to (featuring Fr. Euteneuer) suggested that a Saint's knowledge more-or-less ends at a person's private thoughts (which are reserved to God alone). They also do not know the full mind of God (to count his thoughts we must be eternal (also Psalm 139)).

Omnipotents:
They are not omnipotent. All power which they have are received from God. I would even wager that God denies some of their requests, but I don't have any source for that. I will say that at best Saints hold similar stature as Angels. I also seem to recall that Angels are far from omnipotent.

---

Bonus question (if a none-catholic christian asks them to pray for them do they hear that?):
Asking for the intercession of a Saint is not limited to any group of people or restricted from any group of people. Even if someone is not baptized, a Saint may still intercede on their behalf (or perhaps especially if they are unbaptized). All persons may pray to Saints, and it is possible that any person may be answered. Of course, there is the faith element. If someone does not have faith, then it is doubtful that they will ask for intercession.