Carranger's...not really a parody of Turboranger. The joke is that they were both car shows.
I believe they shared a lot of staffers, too... I want to say Nagaishi directed both series?
Carranger I think can be taken as a general parody of Turboranger, since it approaches a lot of similar concepts but makes them look absurd rather than awesome. It's far too reductive to say that's all Carranger was, though. I think Carranger gets most of the Turboranger jokes out of its system by episode 2 and has moved on to doing much broader parody by episode 4.
I thought the "pop" in the Kakuranger part was a reference to their Adam West-style "bam!" signs/graphics that would come up on screen during fights in that show.
There's also the "old vs new" theme that runs through Kakuranger's more comedic episodes, where the Kakurangers are ultimately fighting something that plagues modern Japan (like, say, people spending too much time in arcades).
Gingaman: if I recall, the JP-dubbed version of Power Rangers: Lost Galaxy made a pretty big splash in Japan.
This is something of an urban legend in this fandom that doesn't seem to be true. The Japanese dub of Lost Galaxy ran on a rather small cable channel, so most Japanese households wouldn't have even had a chance to see it. Gingaman holds the record high for ratings in 90s Sentai, so it's very unlikely that anything airing on a small cable channel could compete with it in terms of pure mainstream popularity.
What I imagine really happened is that die-hard tokusatsu enthusiasts who happened to get the right cable channel found the dub enjoyable and made some "You know, I like this better than Gingaman," comments about it online, which PR fandom then exaggerated over time into "Lost Galaxy was more popular in Japan than Gingaman!"
The dekaranger transformation was obviously inspired by the American one, but I imagine that was more to do with the director just thinking that one looked better, rather than a case of "the Power Rangers fans will totally notice this!".
Actually, I do want to say Sakamoto made some comments to HJU that we should keep our eyes out for a Power Rangers shout-out in that particular episode. So, I think you could say that Easter Egg was intentional, but really more about the director referencing his own past work than Toei acknowledging the importance of PR.
Now if we ever have an episode where the Gokaigers turn into the Zyurangers and Gai accidentally turns into Kibaranger.. that would be funny.
I think this is about the only thing Gokaiger could do that would make me go, "Yes, that has to be a Power Rangers reference."