Yea, the main character has no definite gender so the player can project themselves on them more easily
only to later find out that Frisk is his own thing and you're a separate entity entirely. And nah, the player isn't chara, its made clear on a genocide run that you're a separate entity from him/her, with chara possibly being the only character that actualy directly communicates with the player. Flowey does talk with the player after a true pacifist run, but its kinda odd, since as asriel he admitted to thinking frisk was chara for some reason, with no hint of knowing about the player until you actualy get the ending.
Maybe he thinks the player is chara?
Anyway, why does everyone love to throw infinite labels around instead of just going with "x character likes y character" :v? Why does it matter? Is this tumblr now, where its apparently impossible for a character to exist without a creepy analysis of their sexual orientation and the respective labelling?
And ye, its confirmed that Alphys had a massive crush on both undyne and asgore. She get togheder with undyne because she reciprocates it (in her own way).
Also, I never understood the whole papyrus+metatton ship thing. They don't even interact during the game, and while papyrus seems to want to meet metatton, it may just be because he's the underground's resident superstar. Also don't understand the whole toriel+sans thing, they just seem to be great friends, akin to undyne and papyrus, who clearly really like eachother but in a fraternal, brotherly way.