I do not know the history of interpretation of these 2 issues.
I think the traditional "Christian scripture" indicates confession should perhaps be something of a public spectacle.
The same scriptures seem to (probably) be saying prayer should be completely private.
Beyond that, I do not know the history of interpretation.
I have faint ideas in my head of the history:
("Christian history" always runs the risk of being a history of European Christianity, but allow me)
I know that Roman Christians (which included both Latin and Greek Christians) initially had to confess sins before the entire "congregation".
The Celtic (Irish) branch of Roman Catholicism then had confession privately given to a priest.
(There was a developing split between the Latin West and Greek East of the Roman Church led to differences: Roman Catholic verses Eastern Orthodox)
St Patrick may or may not have been behind the shift to private confession to a priest, but it seems that the Celtic Christians influenced the Roman Pope that they were always loyal to.
The private repentance revolution was a Roman Catholic thingy.
The Protestant issue will surely come up:
The "super-private" 21st century Protestant practice (don't "confess" anything specifically, ONLY "repent" generally, but don't tell any person you "repent", in fact DON'T TALK out loud "but 'have a thinking conversation' to say SORRY to God privately") perhaps had some pre-Protestant precedents, but seemingly came out of nowhere 500 years ago?
That "super-private" 3rd Way is a modern thing when it comes to non-heretical Christians, and might be beside the point when it comes to historical orthodox Christianity (and possibly everything ever called Christianity - orthadox or heretical) of the first 1500 years.
Well, what scripture illuminates your views on these issues?
(Feel free to invoke tradition and/or history as well)