First, we must go to 2011. The album above, アイドル八犬伝☆ホエホエとらっくす, roughly translated to Idol Hakkenden ☆ HoeHoe Tracks, was a remix album released by Tomoo Misato, the game's original composer, at Comic Market 81 in 2011. It's not a complete soundtrack arrangement, but contains a remix of the battle theme with lyrics, a non-vocal remix of the mountain area theme, and three different versions of Kimi wa Hoe Hoe Musume- a standard one sung by HoeHoX (a unit of Satowa Tanaka, Haruka Mikami and Chiaki Mori), a French version sung by Haruko 'Halko' Momoi, known by video game nerds for the WONDER MOMO-i version of the Wonder Momo theme, and a Russian version with sung by Jenya Davidayuk (credit goes to VGMDB for listing all of those) although those foreign language ones are not translations, but more misheard lyrics done in French and Russian styles if that page is right.
Fast-forward a little to 2014, and Idol Hakkenden got a sequel novelisation / light novel, アイドル八犬伝 ~南の島の太陽と星~, roughly translated as Idol Hakkenden ~Sun and Stars on the Southern Island~, published by the Sakuranomori Bunko label of Hifumi which focuses on light novels based on video games, and written by galge scenario writer Jō Shūdō who also worked on novelisations for the Disgaea series. This is a follow-up to the events of the game that, from what I can gather, involves Erika and her friends competing in a game show called Quiz de Hoe Hoe and winning a trip to the magical tropical island, Atsukurushi Island. That's all I can really tell you about it I'm afraid, but the Hifumi page for the book has a little preview including some of the illustrations inside. If you have a Japanese Kindle Unlimited account, you can also read the whole thing for free via the amazon.co.jp product page.
In late 2015, Natsume-Atari- the modern-day equivalent of Natsume who owns their original IPs (and has nothing to do with the other Atari, the one that's Infogrames' shambling corpse dressed up as Atari) ran a popularity contest, roughly translated as the 'Road to 250 Titles' campaign, for their original games such as Abadox, Shadow of the Ninja and, of course, Idol Hakkenden. Fans were asked to vote for their favourite from a selection of ten via Twitter, with a lottery for prizes such as the remix album Natsume Game Sound History 1988-2009 and Natsume-themed mugs and t-shirts. Surprisingly, the winner, by something of a landslide, was Idol Hakkenden with 201 votes (Touhou Kenbun Roku was 2nd with 137 votes, Wild Guns was 3rd with 103 votes and this game would get a remake the next year with Wild Guns Reloaded). If there's a lesson here, it's to never underestimate the power of fictional late '80s idols. Even against the might of Wild Guns, they'll crush all opposition. (Thanks to @gosokyyu for digging this one out for me! I was struggling to find it again.)
Finally, the GAME IMPACT stuff is pretty confusing and sprawling, but let's try our best.. GAME IMPACT is a group that hosts retro game events across Japan, and has had at least two events related to Idol Hakkenden alongside a bunch of different collaboration goods related to the game. The first was held in Hiroshima City from December 4th to December 11th 2016 and had things like a gacha machine with can badges with several different designs, original drawings by Kondo Yutaka, the original planning document by Ando Naohiko and original costume concept art for Erika, as well as a reference book including artwork and interviews. The second was held in Shinjuku from December 9th to December 10th 2017 and, as well as the previously displayed items, also had panels with a lot of the staff who worked on the game including Kondo Yutaka, Ando Naohiko and Tomoo Misato, and an absolute truckload of merch. In fact, while there's a list of items you can buy direct from GAME IMPACT over here, it doesn't quite cover everything that was available at the event! Some of those items include two new albums- one a follow-up to Idol Hakkenden ☆ HoeHoe Tracks featuring unused tracks and maybe remastered demo tapes (sorry, can't confirm as there's no sample available) and another featuring FM synth remixes of a selection of tracks from the game, which you can hear a sample of on GAME IMPACT's YouTube channel- a 30th anniversary booklet including concept art for backgrounds and characters, pastries with Erika on them (!), stickers, keychains, and prints of original character concepts for Erika herself. Everything a true Idol Hakkenden stan could wish for.
Created by a group called the Woolsey Fan Company- named after famous Squaresoft translator and localiser Ted Woolsey- Pop Star Debut, available here on RomHacking.net, is a completely different translation of Idol Hakkenden that isn't really a direct translation, but more a localisation of the game, eschewing an accurate replication of the Japanese text into English for a much more loose one in line with how games were released in overseas markets back in the day. This means changing the entire setting of the game from Japan to a vaguely Western location (at one point a character refers to Pemberley, the fictional British setting of Pride & Prejudice) and renaming pretty much everyone (and even changing someone's gender- Misao is now a nerdy boy called Liam) and everything to make it more English-friendly, which includes a significant amount of graphical changes for things like the girl who gives you the clue to defeating the youkai in the mountains (now the ghost of a deceased general). Some of the scenes, such as the bomber in the concert hall and the ghost commune, are softened up, stuff like the ashtray and frog sweat are renamed to less weird things, and even plot points are changed- the secret of the idol producer in Act 3 goes from having an affair with one of his idols to enjoying tea parties with dolls and watching Little Ponies on TV.
Unfortunately, this is not the optimal way to play the game in English. I'm at least intrigued by the concept of it- a 'what-if' project like this is fun in its own way, and I'm thankful this is at least based on a game that already has a fan translation- but some of the changes are not for the better. Many of the little puzzles in the game are made far too easy- for instance, the clue for the last puzzle of Act 3 in Idol Hakkenden is to 'turn the lakebed into a field of flowers', which through a bit of logical thinking and experimentation, you can deduce the solution to; in Pop Idol Debut, you're simply told, with no room for interpretation, exactly where to go and what to obtain to progress. This sort of thing strips a lot of the charm out of the game, which I suppose is part of the 'what-if' nature of things, but still. It doesn't help that this has several text overflow errors which would never fly in a retail game, and even the translation's core conceit of sticking to '90s Nintendo guidelines is somewhat ignored as the stun gun and pistol are still in the game, unchanged. I figured Nintendo wouldn't let a kid play with an actual gun in one of their games, but what do I know, eh? I would personally stick to the other translation, but this is interesting to at least observe if you're really curious.