1) To swim, tap near Naija, to burst, tap further away. (At least it's like this using a mouse, so i assume it must be the same for touch controls).
And yes, you have to burst in beast form to eat stuff, swimming only isn't enough. This is intended.
2) When you are on a seahorse, sing to control it. You'll be a lot faster than normal, especially if you're wearing the seahorse costume.
3) Probably. Using singing only (= mouse only) to switch between forms is a lot harder than using quick-keys on the keyboard (Which i had to use for all optional bosses except nautilus prime, i have to admit. Maybe didn't try hard enough, though). But pointing a finger at something should be faster than pointing a mouse at something, so it may even itself out a bit.