Note: If you're citing information post-Schism, I'd prefer the Orthodox side of things.
Canonizing officially recognized "Saints"
Adopting patron saints
Using icons in Church and prayer at home
Praying to saints (either the apostles, their patron saint, or others)
The high level of regard that Mary has - praying to her, venerating her, the various beliefs surrounding her (perpetual virginity, immaculate conception, etc.), etc.
To further clarify, here's a fictional scenario putting these practices in a modern context. If that's not okay for this sub, I'll delete it:
Nikolai is born to Russian parents on December 6th and baptized into the Russian Orthodox Church (or the Russian Orthodox Church Outside Russia, depending). For these reasons, his patron saint is Saint Nicholas, whom he commemorates on his birthday. Over the years Nikolai gets icons of Jesus, Saint Nicholas, Mary, and the Apostles. These icons sit in a "prayer corner" of his home where he lights candles and prays to them. In addition to God and St. Nicholas, he venerates Mary very much with various prayers at home and at Church.
Hopefully this is all okay. I've tried asking this question (and related ones) before, but either due to the format, nature of the question, or whatever else it never got answered. So I just keep deleting it and trying again :)
My answer is very limited in scope. I cannot speak to Orthodox practice at all, so my answer will only address the Catholic position. Further, I will only address Marian practices, and I will not tackle the origins either as my expertise only stretches back so far.
Immaculate Conception
This dogma of the Catholic Church was defined by Pius IX in 1854 via the proclamation contained in of Ineffabilis Deus. In that document the pontiff gave the justifications for the definition. That definition reads:
We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful.
Declaramus, pronuntiamus et definimus doctrinam quae tenet beatissimam Virginem Mariam in primo instanti suae conceptionis fuisse singulari Omnipotentis Dei gratia et privilegio, intuitu meritorum Christi Jesu Salvatoris humani generis, ab omni originalis culpae labe praeservatam immunem, esse a Deo revelatam, atque idcirco ab omnibus fidelibus firmiter constanterque credendam.
Fifty years later, Pius X commemorated Pius IX's document with Ad diem Illum Laetissimum which expanded upon the reasoning given by Pius IX.
Assumption of Mary
We have yet another Pius to reference: Pius XII. In 1950 he released Munificentissimus Deus, an Apostolic Constitution that defined the Assumption of Mary. Along with the aforementioned Immaculate Conception, these two instances comprise the use of papal infallibility since that dogma was defined in 1870. Once again, I will rely on the pontiff's own words for the justification of the dogma.
I apologize for not being able to me more expansive. My own limits in expertise as well as some other obligations dictated a shorter answer than I would have liked. As always, followup questions from OP and others are encouraged.
Just on the lack of an answer after several repost: You're quite welcome to keep positing it (though obviously not incessantly).
Even though church history is my area, I have never traced these particular issues through in any great detail. I suspect that you just have not had a constellation of a knowledgeable willing and available respondent turn up to answer for you yet.