1) I don't think I would have a problem with love triangles if the characters would be writen better, the main issue is the lack of understanding the characters and the love triangle becomes the only thing that they care about, the decision of who is he/she gonna choose is the only important thing in the story while the character's aren't really explored that deeply.
I also always find that it makes the characters in it very unlikable with the frustration of "I can't choose" and one person being way too clingy and all the other typical stuff, this can work in your favour if it's intentional but it's hard to do.
2) Take the time and write characters better, make sure they have other things they're worried about other than the love triangle, it can still be a major plot point in the story but it shouldn't be the only thing your character thinks and talks about all the time. Make sure they are interesting outside the love triangle and even when they're not together, and they have their own flaws and their own dreams they want to acheive, like actual people.
I think whether you make it an actual triangle (A loves B, B loves C and C loves A) or make it poly or do something else with it, while it might be interesting, some of the main problems will remain unless you work on the characters first.
3) I don't know if this is an example of a 'love triangle' but Fruits Basket but I can't say why since it's a spoiler, but it's basically not as it's seems and the characters are just so well written and it ties into the story really well.