How do they react if they get low in health? Do they flee or kneel?

How do they react to werewolves?

Thanks

My dog drowned under some ice, so I don't know what he did in his final moments.

Now, my companions are two legged.

Haven't noticed a consistent poor health reaction but if you talk to them, their health bar shows. I've had Vigilance along for several levels (45-48) but I have had to use a restoration spell on him several times after combat. And have been cautious about taking him into truly dangerous places. Usually have him stay outside of dungeons.

Is there a quest that involves animal followers or can one get a dog to follow right from the beginning of the game? How does one get a dog to follow?

To answer the OP's question, the Dog followers will do the "laying down dog" animation when they get low on health. They also appear to lose combat focus from enemies (meaning they are ignored when badly hurt) just like your typical humanoid followers do when they get very low on health.

And just like the humanoid followers, they will die if they get hit by a stray arrow/spell when they're very low on health. I've also noticed they regain health much more slowly than the humanoid followers do after combat.