So, does one describe the natural state of that "special type of magical beast?"
A CR 1/4 or lower beast. To quote the Unearthed Arcana article it’s from:
“When a primal beast is met apart from a Beast Master, the creature takes the form a regular beast of challenge rating 1/4 or lower, as determined by the DM.
The player decides. To quote the UA:
“When choosing such a creature, you decide whether it is a Beast of the Air or the Earth, and *you determine its appearance.”
In the wilds (presumably in the natural habitat of the CR1/4 monster the DM determines it is). To quote the UA:
“A special type of beast awaits a Beast Master in the wilds, a creature whose lineage stretches back to the beginnings of the world: a primal beast known as a Beast of the Air or a Beast of the Earth.”
How does it naturally behave?
Unclear, except for the fact that it craves the companionship of a Ranger. To quote the UA:
“Such a creature seeks out the type of companionship that a Beast Master offers, ready for the two of them to battle the imbalances in the natural world.”
Is it a mimic that can only change form when not bound by a ranger?
Well, it’s not a mimic, that’s a different kind of monster entirely. But, it might be able to chant form when not bound by a ranger, if the stories are to be believed. To quote the UA:
“Stories describe primal beasts that mystically change form to align with the spirit of their companion.”
So a BotE pretending to be a pony can also give an enemy the finger?
Well, no, ponies don’t have fingers. It could probably give the hoof. Maybe could if it changes form to a best that does have fingers.
I'm not sure those things are "cosmetic." Giving an enemy the finger can have real, in-game effects. If a character with red hair who walks into a town full of red-head hating ruffians, is having red hair merely cosmetic? Moreover, if a PC is infected by poisonous lice, the ability to remove them effectively is not cosmetic at all, but is instead a life-saving ability.
Thart’d all be down to DM discretion.