We pray, i.e. mediate for one another, because we are all, living or deceased, united in the Vine, which is Jesus the Lord! (Jn 15). He is the One Mediator between God and man, who enables us, "in Him" and "through Him" to mediate...in other words pray... for one another, even though He knows our needs even before we ask. All who live "in Christ" are alive in Him! Jesus said we would "never die" if we "abide in Him". St. Paul said death has no victory and can never "separate" us from the love which is in Christ. It can never rend in two that which is always and forever one in Him, the Body of Christ. We are family who pray for one another as our Lord commands. We are family for time and eternity. Death has no dividing power over us in Him. That is why the souls in Heaven never cease to pray and intercede for those who are still undergoing the spiritual trial on earth (Rev.5:8; 6:9,10 etc.). How could they simply forget us? The book of Revelation shows our Lord totally concerned, as one would expect, for those still undergoing the battle on earth. The Saints, those who "have overcome"...could they, unlike their Lord, forget those still undergoing the trial?
When a Protestant friend asks another Protestant friend to pray for him or her it is presumably done. But why, the Catholic might very well ask. If Christ is the "one" mediator between God and man, what need does anyone have of another's mediation, another's prayers? Why wouldn't the protestant simply tell others just to go directly to God Himself? It would seem to make sense. But "God's ways are not our ways". We "mediate," pray for others, because God commands us to (James 5:16 etc.) in Love! God doesn't need ours prayers, i.e., our mediating for someone else, but He commands them. It is the mystery of love, rooted in and grounded upon our Lord's own Love and Mediation shown in His atoning Cross. Our inferior mediation for one another does not prejudice the absolute uniqueness of His eternal mediation. It participates, by sheer grace, in it: "Through Him, with Him and in Him" as is said in Holy Mass.
So of course Catholics ask Mary to pray for us. Especially Mary, so intimate with her Son as to have, by grace, given Him life, His time-and-space humanity, by her own heartbeat and blood in the womb! His Blood that was shed for us all.
All we Catholics ask is that if you reject us, it is not for the wrong reasons.