Mavel vs Toei
 

Does Marvel/Disney share the rights to Battle Fever J and Denziman with Toei or is it a sole Toei property? Also, now that Japan's Spider-Man is being brought to the USA by Marvel, will this open the door to Battle Fever J and Denziman comics (for modern audience assuming if there were or were not comics for US audiences in the 1980s)?

No it won't open the door. Leopardon & Spider-Man being in the book is just a one-off reference if anything. Simply because Spider-Verse involves every spider-hero in the multiverse. There is zero chance that american Battle Fever J or Denziman comics will ever be a thing. There simply isn't a market for that.

Optimistic much?

Japanese Spider-Man showing up was fan service to the hardcore fans. Den-O is right since a comic based on Battle Fever J and Denziman won't likely sell well since it's based on a niche TV show from over 35 years ago. I think the people would likely buy into a Battle Fever J comic are the hardcore Toku fans and Sentai/Power Ranger fans like us. Besides that, it's not really enough.

Yet everyone is still ignoring the first part of the question

It's just being realistic. Marvel may have helped produce the series, but considering they didn't use any previously established characters, I doubt Marvel/Disney has much stake in BFJ or Denziman.
It was just a fun little nod to the people who'd get it.

But does Marvel/Disney share the rights with those 2 sentai series with Toei or not? That's the main question.

Very unlikely.

From what I heard that Battle Fever J and Denziman fan subs get taken down mostly in part by people a part of the Marvel Comics team.

More like not at all.

Unfounded rumors in a fandom full of unfounded rumors.

I haven't heard such claims, so I wouldn't know.

I don't think anyone at Marvel really cares about the Toei co-productions enough to actually do anything with them. The Supaidaman thing was just something that tied into their Spider-Verse story, which is tying in every single version of Spider-Man they have access to (which apparently excludes some of the Sony co-productions, although I'm not sure how much of that is rights and how much is Marvel being a dick towards companies that still have some of its film rights).

Between this comic and Marvel formerly having the show streaming on their site, I think it's safe to say that they still own some of the rights to Toei's Spider-Man. I'm not sure if that holds for Battle Fever J, Denjiman, and Sun Vulcan. The latter two didn't even have any actual input from Marvel, despite the co-credit. Plus they're part of Super Sentai and I don't know how much of that Saban holds the license to (probably all of it, given all of Super Megaforce's "New Powers").

In any case, there is absolutely no reason to think Marvel would bother making new comics for Japanese TV shows from the mid-70s that very, very few of their readers have ever heard of, much less seen. That's like seeing the X-Men anime and expecting Madhouse to make an anime based on US-1.

So does anyone have a device that lets you go to alternate dimensions? I want to go to that one reality where Avengers fight side by side with Battle Fever J just for the heck of it.