1) "The United States flew nuclear armed bombers to the borders of the USSR 24 hours a day."
That is true. One of the linked-to examples is https://en.wikipedia.org/wiki/Operation_Giant_Lance "These bombers were to patrol the Northern polar ice caps to survey the frozen terrain, whilst armed with nuclear weaponry.[4][6][2] The patrols consisted of eighteen-hour long vigils, which were executed with the intention of appearing as suspicious movements from the US."
2) Do Russian planes military fly close to the US on a more than yearly occurrence?
Yes. That is without a doubt, as you have show.
3) Do US planes do the same?
Yes. https://www.airforcetimes.com/news/pentagon-congress/2014/09... mentions "China denied any reckless flying and said it would continue responding to U.S. surveillance flights off its coast, which Beijing believes are a threat to its security." and famously https://en.wikipedia.org/wiki/Hainan_Island_incident
For Russia, https://www.rferl.org/a/russia-says-fighter-intercepted-u-s-... "Russia says a fighter jet intercepted two U.S. military surveillance planes in the Black Sea" and of course there are currently a lot of NATO surveillance flights watching the Russian border now.
https://en.wikipedia.org/wiki/Lockheed_EP-3#Other_incidents lists two close passes of a US EP-3 by a Russian Su-27, and one by a Venezuelan Su-30.
4) Are any of these to preserve "normative freedom of movement rights"?
No.
5) Do any of them "usually breach airspace generally considered sovereign"?
No.