There are a number of serious problems with the concept of the Rosary.
First, "Hail, Mary", is simply something the angel said to Mary. There's no indication it was a prayer or that we need to be reciting it.
Second, most translations don't translate the words as "full of grace" - the Greek simply means, "favored one" or "highly favored one", or "who has found favor", etc. This simply means that Mary was favored by God in choosing her to bear the Messiah. There's no indication that she had any special place or power outside of this status.
I'm going to digress on a tangential issue: "Grace" as Catholics talk about it, stating that Mary is the "distributor of all graces", etc, makes grace sound like something akin to "the Force" in Star Wars.
It's as if "grace" is a thing, some force or power, that you get in response to all the works you do. There is absolutely nothing Biblical about that, and in each and every place that Paul talks about grace, he is talking about the unmerited and undeserved love, or favor, of God. Grace is God's unmerited love toward us, who are unworthy of it, and faith is the tangible gift that is the end product of that grace. But in Catholic doctrine grace seems to be some kind of "power" or "force" that you get filled up with - like a video game...I'm "low on grace", because I sinned...so I hit the magic Rosary pellet and bingo, my grace level pops back up... (I don't mean this to be mocking, it's the best analogy I can come up with - that's truly how it seems to me).
Third, Jesus clearly treats his mother as he would anyone else. He doesn't show her any special standing or favor above anyone else. When Mary asks him to do something about the wine situation at Cana, Jesus doesn't show her any special deference, in fact, he almost rebukes her, with a, "what does this have to do with me?" - in other words, "Why are you bothering me about this?"
When Mary and Jesus' brothers show up to "get him", when they think he's gone off his rocker, what does Jesus do? The people tell Jesus that his mother is outside with his brothers and want to speak to him. Does Jesus jump right up and rush out to give her a big hug and kiss, or does he call her "highly favored" or treat her in any way as special or above anyone else? No, in fact, it's just the opposite. He doesn't go out to meet them, he stays right where he is:
Matthew 12 "48He replied to him, "Who is my mother, and who are my brothers?" 49Pointing to his disciples, he said, "Here are my mother and my brothers. 50For whoever does the will of my Father in heaven is my brother and sister and mother."
There is most definitely no special favor shown to Mary or his siblings, by Jesus. In fact, this goes to demonstrate a central theme of his ministry - the equality of all believers in the eyes of God. We are all equals. The priesthood of all believers is based on this same principle. We don't need priests between us and the Father. Jesus opened the door himself, it's the very reason the curtain of the Temple was torn in two. Jesus opened the path for us to come directly to the Father, through him, in his name, and we don't need intermediaries (as Hebrews, in fact, says). Jesus did not come to replace one hierarchy and priesthood with another. He came to do away with it.
John 4 "21Jesus declared, "Believe me, woman, a time is coming when you will worship the Father neither on this mountain nor in Jerusalem. 22You Samaritans worship what you do not know; we worship what we do know, for salvation is from the Jews. 23Yet a time is coming and has now come when the true worshipers will worship the Father in spirit and truth, for they are the kind of worshipers the Father seeks. 24God is spirit, and his worshipers must worship in spirit and in truth.""
No more Temple. No more Priesthood. Jesus is our "great High Priest" according to Hebrews. And as 1 Timothy says,
1 Timothy 2, "5For there is one God and one mediator between God and men, the man Christ Jesus, 6who gave himself as a ransom for all men—the testimony given in its proper time."
Jesus might have established a church (of all believers) but he did not come to replace one priesthood and hierarchy with another, between man and God. And the Scriptures make that pretty plain in many spots (the curtain of the Temple being torn in two being the biggest and most obvious example).
Fourth, there is no evidence that those who are dead, and "alive with Christ", can hear or see or have any awareness at all of what is happening on earth. Even the Old Testament points to this. The one verse in Revelation that Catholics point to, is as big a stretch and reach as you could possibly make, and it seems absurd, on its face, as the basis for the argument about "prayers to Saints". Of course we can ask persons on earth, our friends and family, to pray for us. They are alive and they are with us and we know they can hear us if we ask them. There is no indication whatsoever that any soul that has passed on can do the same. Nothing in Scripture, either. In fact, what is in Scripture, is the constant (and consistent) admonishment not to talk to the dead, not to consult with Necromancers or anyone (witches, those who practice divination) who "consults the dead".
Fifth, the Psalms you quoted are merely Psalms of praise to the Lord, they are not "prayers" to angels or saints, unless you really want to stretch it, and I consider it stretching it.
Sixth, in investigating where all of the Mary and Saints thing came from, historically, some pretty clear things start popping up right away. This entire practice (and doctrine) developed out of people's fear of God as a "judge". God and Jesus, as part of the Trinity, were seen as judgmental, angry figures who were so Holy that one could not imagine talking to them directly. It was this harsh, "father figure", "king and judge", image of the Father and the Son that led people to look for a "softer" image to act as a go-between. So Mary (and the Saints) became a focal point - they became the human face - something people could relate to - a softened, motherly and brotherly set of figures that people could "ask to intercede". Afraid to go to Dad themselves, because he was a harsh authority figure, they decided to "go ask Mom".
It became readily apparent to me, anyway, through even the most cursory investigation of the matter, that it was this psychology in the early Church that led to the development of a "need" for some figure like Mary or the Saints to "intercede" with the harsh, judgmental, and angry Father (and Son). One couldn't imagine going to Jesus themselves, who was going to be their judge someday, no, no...one must go to his Mother to soften the blow...to talk to him for us....even though what the Bible says about Christ goes directly against this (1 Timothy 2:5, and the other examples up above - the curtain being torn in two, etc). Jesus is our mediator. We can go directly to him and more importantly, we should go directly to him.
All this doctrine of Mary and the saints came from early Christian fears, from the image of Jesus they had constructed. Jesus is going to be our judge. But he is not a figure to be feared in that sense, he is a figure of love and mercy that we should, in fact, run to - to go to in all things, and if we truly have faith, if we believe, we should never fear that. I don't need the souls of dead human beings, who now are alive in the presence of the Lord, to do anything for me. No one does. We only need Christ Jesus. That's the only person I feel the need to go to.
Okay, this got very long...
As it happens, I read Greek (studied Classical, but Koine is not difficult after 5th c. Athenian and Homeric Greek, just different).
The translation 'full of grace' is a fairly accurate translation of the Greek word kecaritwmenh. It's a verb, and a particular type of verb - a perfect passive participle, which means a state that has continued for an indefinite time and continues in the present and for the foreseeable future. "Completely and for always graced" is, however, a translation that is not very graceful in English.
That doesn't mean, of course, that the grace bestowed upon Mary by God from always was in any way due to her personal merit. But it stands to reason that God would make sure by His own power that the woman who was chosen to bear Him in her womb for nine months and entrusted with His earthly rearing would be pure and holy, the new Ark of the Covenant. ("No special place or power outside of this status?" What on earth could be more special or powerful than to have the awesome and unbearable responsibility of bearing and raising God? Of course Mary had to have divine help and grace to fulfill this otherwise impossible task!)
You have seriously misunderstood the Catholic concept of 'grace'. Your description is downright creepy, and totally unlike anything I have ever heard from a reputable Catholic source (of course, there are plenty of misguided and misinformed people around in the Catholic church, like every other church around, but you can hardly judge the doctrine of a church by one or two confused laymen, especially when the actual belief is laid out plainly in the Catechism for all to read!)
When a bunch of busybodies interrupt you while you're teaching and tell you your mom is outside, and you correct them for interrupting you (and incidentally for missing the entire point of what you are saying), you are not dissing your mom, who isn't there to hear. Neither are you dissing your mom when you correct a bunch of female groupies who are engaging in the usual over-the-top Middle-Eastern hyperbole ("blessed is the womb that bore thee . . ") without thinking about what they are saying.
Consider that, when Mary asked Jesus to help out an embarassed bridegroom at Cana, he remonstrated with her but helped anyway, with something as mundane as running out of wine and the resultant loss of face at the wedding . . . . and he did not say, "what does this have to do with me?", he said ti emoi kai soi - "what does this have to do with you AND me?" - why is this important to us? But - as he praised the response of the Syrio-Phoenician woman to his apparently disapproving question about dogs and bread, here he approved because he went ahead and did as Mary asked.
Consider also that, since Jesus was perfect, he perfectly fulfilled all the Commandments, including "Honor thy father and thy mother."