Kind of. It's also to have balanced muscles to prevent injury. Front squat helps back squat and back squat helps front squat. Generally your front squat should be about 80-90% of your back squat, maybe 95%. In the end for a weightlifter it definitely is more important than the back squat.
That doesn't make sense to me. As long as you are on your heels and keep your back as straight and tight as possible, then you are using the quads to get up. Personally I can only understand not being able to have a muscle work if its one you don't use often or at all. For example there are dozens of muscles on our face and head that I can't use cause I don't know how and other people can. I also for quite a while couldn't do a proper shoulder shrug and only recently can I do it rather fast. But your quads are muscles you use very often, if you've been lifting for a while they should work properly!
They are indeed more posterior chain compared to the front squats. And aside from helping get the other squats up(they still do use the same muscles, just to a different degree... plus you know, variety is good no matter if you are oly lifter, powerlifter or bodybuilder. There are exceptions but those are very specific), you certainly need a strong posterior chain no matter what sport you are in and especially olympic weightlifting, mainly for cleans that are going to throw you down in the hole and if your back isn't strong enough, very likely your elbows will drop and you'll have to drop the weight or you'll keep it and have to stand up with a rounded back.