Do all teams need a dancer?

It really depends on your playstyle. If you enjoy the extra mobility, then sure, go for it. If you feel that you don't need them, then just avoid them. I use them because I love the mobility, but that comes with my heavily offensive playstyle. So, once you figure out your niche in the game, either as a hyper offensive player or a much more defensive player, you will know the answer to you question.

Not really. While a dancer is always useful, they are weaker at combat, and if you plan to hit tier 20 and stay there, a dancer is a liability.

Dancers are useful, but in arena assault, I often find myself forgoing dancers in favor of healers. The only real exceptions being Olivia, who's actually able to kick some butt with a Wo Dao, and Ninian, whose sole purpose outside of dancing is providing dragon buffs.

Olivia is readily available and is a beast. Working on 5*+10

At higher tiers theres a lot of armored units and she just cuts right thru them. Green dragon robin is laughably bad against her with the armorsmasher+ equipped