They are not parody openings, they were made for the reruns. Yorinuki Gintama-san is basically Just reruns of the best episodes with new openings and better quality (not better animation, just quality) The "Bakuchi Dancer" opening that you found familiar, plays on Benizakura Movie, it's on top 10 fights video
Kagura is 14 at the start of the series, 16 at the end, and 18 in the second movie ( the opening where she has the really long hair) lol. Shinpachi is 16, 20 in the 2nd movie and 18 at the end of the series and Gintoki is 27ish at the start, and believed to be 29 or in his early 30s by the end of the series. He was actually one of the first/few older protagonists is Shounen. Sadaharu (the dog) is introduced by episode 10 :)
These are the rerun OPs ("Yorinuki" = "Best Of"). The parody OPs, off the top of my head, are OP5 (Katsura ver.), OP8 (Paint ver.), OP9 (Fail), OP12 (Kintama), Gintaman, and Mantama. You might've been recommended to react to both by different comments. Kaze no Gotoku (Yorinuki OP2) is one of my favorites though.
I'm pretty sure there are 6 Ops for yorinuki gintama, because I didn't see the Chico one, that's probably my fav out of those. Fyi the title is "Kyou Mo Sakura Mau Akatsuki ni"
These are not the parody openings as others mentioned, and they are parody in the context that sometimes the show will play a joke opening instead of the actual one, so they are official. But I feel like they are funnier in context. Since you're already watching the show, I'd say to skip reacting to them separately to get surprised when they actually show up. Just my opinion though.
This opening's not parody, full offical Yorinuki gintama-san, series the best episode of Gintama. And you missed the special op in the main series, i mean the Gintama Dragon ball op and another songs too. And the another verse of the main op, i mean the op 17 and op 20 have4 diffrent version, and op 16 have 3 diffrent version.