1) While it may be tempting to deny that birthdays are rooted in superstition, magic and pagan religious customs--almost everything I read backs this idea. People (in general) evidently began celebrating birthdays in order to keep away bad spirits. Granted, not every culture has the same practices for birthdays or how to observe Christmas (etc). That's an understatement. But I'd like to see an early culture that observed birthdays for non-religious or non-superstitious reasons. I have not found one yet.
2) Ancient Jews and Christians roundly condemned the observance of birthdays at one time. Origen is a famous example: he wrote that not one "saint" (holy person) observed a feast on the day of his birth. Furthermore, Clement of Alexandria spoke ill of those who speculated about the Savior's day of birth. See John Davidson, The Gospel of Jesus: In Search of His Original Teachings, page 131. Another patristic writer who spoke against birthdays was Arnobius of Sicca; see Adversus Gentes 7.34. It's also possible that Philo condemned birthdays while we know that Josephus did.
"Nay, indeed, the law does not permit us to make festivals at the birth of our children, and thereby afford occasion of drinking to excess" (Josephus. Translated by W. Whiston. Against Apion, Book II, Chapter 26. Extracted from Josephus Complete Works, Kregel Publications, Grand Rapids (MI), 14th printing, 1977, p. 632).
One writer examines both sides of the issue from a Jewish perspective, but it seems that all of his examples to uphold the celebration of birthdays are late, since they date from the 4th cent. CE onward. See http://louisjacobs.org/library/articles/birthday-celebrations.php
3) To my knowledge, wedding rings did not originate from pagan religious sources. I read an article on this point years ago, but would be happy to see additional research on the matter. I choose not to wear a wedding ring anyway, but not for religious reasons. It's a matter of conscience IMO.
4) On circumcision, we have two issues at play. What are its origins and why did God command Abraham to do it? Scholars point out that the issues surrounding circumcision are more complex than the subject may first appear. There's no necessary B-line from Egypt to Israel as far as circumcision is concerned; secondly, it's far from clear that the Egyptians started practicing circumcision because of religion.
In a journal article, "Circumcision in the Ancient Near East," Jack M. Sasson argues that it's very unlikely the Israelites or Phoenicians adopted circumcision from the Egyptians. After reviewing some archaeological evidence from Egypt, he reports: "Thus one can note a basic difference between the Israelites and the Egyptians in the surgical process involved in circumcision. Whereas the Hebrews amputated the prepuce and thus exposed the corona of the penis, the Egyptian practice consisted of a dorsal incision upon the foreskin which liberated the glans penis. The Old Kingdom reliefs at Saqqara clearly demonstrate the results obtained by the Egyptian surgeon." See JBL 85 (1966): 473-76.