1a.) Not sure when baptism of babies started; I’ll have to defer to other students on that.
1b.) I’ve never heard of any children simply taking Mass / Lord’s Supper per se, though, no matter how old the Christian group is. Not without a clear profession and confirmation of faith – my seven-year-old niece was baptized a few Sundays ago and so can take the Lord’s Supper now, for example, but she had made a profession of faith at 5 and we held off to make sure she knew what she was doing. The old Catholic groups (up to and including the Anglicans), so far as I’ve ever understood, are far more regimented than that about when and under what conditions children are confirmed and so officially permitted to partake in the Mass. Maybe this is a local thing where you are?
2.) Constantine didn’t change much. Constantine per se didn’t make many changes at all, though he acted as executor for the college of bishops. He introduced some trivial things like changing and regulating the holidays, notably Christmas. (The evidence from the time is that Christians before then celebrated it in the autumn around the time of the Feast of Tabernacles, but we don’t have a lot of evidence when exactly Christians celebrated it.) He found ways to integrate the church hierarchy into the officially civil cultic life, which tended to involve helping ease people into accepting the newly legalized religion by assigning parallel titles they were already familiar with (like “pontifex maximus”, greatest bridge builder).
Becoming a legally protected religion with preferential treatment at Imperial levels tended to change the tone of Christianity, but again for most of the 4th century the Arians were in the driver’s seat. I’m not blaming them for what happened either, but they show that the 4th century mostly wasn’t when a particular kind of Christianity latched permanently into an Imperial form. (Otherwise the Arians would have never been able to overtake orthodoxy at the Imperial level, and orthodoxy would never have been able to re-overtake Arianism and neo-Arianism at the Imperial level.)
3.) I do think Marian honors picked up substantially in the 2nd century – not sure about the 1st in the extra-canonical docs. Obviously there isn’t much of that sort of thing in the canonical texts, but there are hints of it in RevJohn and in the technical language used by the angel at the Annunciation in GosLuke. The term “God-bearer” goes back a long way, too. Praying religiously to Mary and the Saints seems to start rather later; there’s nothing about that in the canon, and I don’t think anything about that for a few centuries afterward. A lot of it comes from the expectation that the servants chosen by God continue helping even more after death, which is a respectably cooperative belief (even if I don’t agree at all with the religious venerations that were developed along the way.)
4.) Icon-making has progressed as an art form. I’m sort of doubtful they existed in more primitive forms – I know Christian art existed, but I haven’t seen evidence they were treated as icons are religiously treated. But I wouldn’t be upset to learn otherwise.
5.) On one hand, so long as we’re worshiping in spirit and in truth, I’m not sure God cares overmuch about the details. On the other hand, God seems to care a lot about some details in the scriptures, even if not to the degree of detail found in advanced liturgicals. And if worshiping in spirit and in truth is important (which it is), then details which help a person do that would be proportionately important, even though not strictly necessary. Liturgy helps get across fine points of doctrinal truth (or what is believed to be doctrinal truth anyway) to people who don’t have the time, opportunity, and/or talent to work on the theological math for themselves. That’s true about icon usage, too. I may protest about iconic veneration, but I appreciate the basic concept.