Are Mother Mary, Saints and Angels omnipresent like God, to listen to prayer requests of the faithful from different locations on the planet at the same time?

Only God is omnipresent. Mother Mary, the Saints or the Angels are not omnipresent. But, they can and do listen to any prayers addressed to them from anywhere in any language. This is not because they are capable all by themselves, but rather God makes them “accomplish abundantly far more than all we can ask or imagine” (Ephesians 3:20). It is God who empowers them.

Bible says when we are in Christ, we are one body with Him (Romans 12:5), and we are branches of the one true vine (John 15:5) and not even death can separate us from Christ (Romans 8:38). The body of Christ, the Church, is made up of both the living (those on Earth) and the dead (those in Purgatory and Heaven), together forming a spiritual solidarity called the communion of saints. And since those in heaven are in perfect communion with God, they also have communion with us through God. Also those in heaven are not restricted by space and time like us on earth.

Now that we have established that the whole Church is in the mystical body of Christ, let’s look into how the human body functions. Suppose there is a wound in one part of the body the whole body becomes aware of it and prepares to help in the healing process. For example platelets adhere to tissues around a wound, forming a blood clot, sealing damaged blood vessels and the bone marrow starts producing more white blood cells to combat possible infection of the wound. All of this happens because every single organ in the body is joined to the head and receives the required information from it. Similarly, those in heaven, who are in perfect union with God, can hear the prayers of the faithful through Jesus Christ, the head of the body  (Colossians 1:18), and obtain for us what is needed as per God’s will. 

We do have Scriptural evidence to back up our claims. One such evidence would be Revelations 5:8 where we find the elders in heaven holding “golden bowls full of incense, which are the prayers of the saints”. If they are indeed offering up our prayers, they also must be aware of them. 

As I conclude this answer I would like to remind all readers that whatever the saints and angels obtain for us, they obtain them from God as the scripture says “every perfect gift is from above, coming down from the Father of lights” (James 1:17).