1) Not a VNIt's been done and you can find a few examples if you look back far enough. The OG Harem started by ker in 22011 (funny to look back to 2011 /hgg times when "Harem" was a good enough name that wouldn't get confused with 15 other games) it had 8 years of constant updates then got abandoned in 2019. Afterwards it had several fan remakes that also got abandoned, surprisingly had ker return after a 3 year hiatus, admit that after all he went through he didn't want to start remaking Harem solo with an 11-year old engine and finally resulted in ker teaming up with Fylokon Games to give us the game we have today which is made in a new version of RPGMaker and Koikatsu and is getting regular updates which you can play here: https://f95zone.to/threads/harem-rpg-remastered-4m1-1-fylokon-games.158499/
So yes it happens, but it's rare and comes with many downsides. Like the fact that in current oversaturated market a 13yo story feels generic and the fantasy wish-fullfilment harem game's been done to death in the meantime with much smoother gameplay and much higher-rez graphics. I still enjoy it but I admit a big part of why is the nostalgia.
2) Doesn't look all that successful, though it's definitely not an outright failure.
3) Your example of a fan made continuation going on to be successful is.. a remake by the original dev in partnership with another? -_-
The rule with fan remakes when it comes to VN's (especially abandoned VN's) is that they're garbage, and will last the initial release plus an update or two at the most. I can't think of a single exception, but I'm sure they're out there. That said, I don't think you did your point any favors by choosing the one you did.
I wish that weren't the case because there's a ton of games that had amazing starts only for the original devs to just disappear, or start off down the milking rabbit hole. Still, it makes sense - competent writers tend to want to write their own stories, and people who can do decent renders find out pretty fast that writing is a bit more challenging than it might seem.