The Catholic belief is that Christ alone is the judge of our salvation. Indeed, there is clear scriptural teaching that that is so, as your quotes demonstrate.
Intercession is not scripturally claimed to be Christ's alone. We see Blessed Virgin Mary asking Jesus to perform a miracle at Cana, which begins his ministry as a worker of miracles. We see Mary of Bethany and Martha asking Jesus to raise Lazarus, -- the miracle clearly prefiguring salvation of men, -- and even rebuking Him for tardiness. In the Old Testament Abraham pleads with God. Thus not only intercession of the Blessed Mother, but intercession of saints in general are scripturally sound.
Catholics tend to get angry when they are told that they don't read the Bible, or that they repeat what the Popes tell them, or that they do not worship Jesus, etc. Anger is not the best reaction to have, all the more so since the devotion to the study of the scripture is an admirable Protestant trait. Nevertheless, understand that when one's faith, particularly a demanding faith such as Catholicism, is questioned in a rude and ill-informed way, a foundation of one's existence is attacked, and people get very defensive.
"We see Blessed Virgin Mary asking Jesus to perform a miracle at Cana,"
My Bible clearly shows she was no longer a virgin at this point.
"We see Mary of Bethany and Martha asking Jesus to raise Lazarus, -- the miracle clearly prefiguring salvation of men, -- and even rebuking Him for tardiness."
I don't read that passage in John, feeling they were "rebuking" Jesus. Disappointed, yes, rebuke,no.