The Animated Shield says that it
protects you as if you were wielding it.
This strongly implies that you aren't wielding it.
The Monk's Unarmored Defense feature works
while you are wearing no armor and not wielding a shield.
So the use of an Animated Shield shouldn't interfere.
As for proficiency, the only requirement for using an Animated Shield is that you're attuned to and holding one, so this shouldn't be an issue. There is an argument against this, though:
The Animated Shield protects you as if you were wielding it.
Luckily, wielding a shield with which you're not proficient doesn't affect how it protects you; all it does it give you a bunch of penalties to other things.
Since the Animated Shield "protects you as if you were wielding it", and doesn't "give you penalties as if you were wielding it", this isn't an issue.