He did not pronounce the ם in שותים does it normally just run into the next word when the next word begins with another מ like this?
Right now it's very difficult for me to decipher the Audio, I really have to think about it. I hope it gets better with time.
It's quite normal; people don't pause between words to make sure both 'm' sounds are heard individually. It's a matter of experience, I'm sure that with some more exercises you'll get it more easily.
I agree, I didn't hear it at all. I guess I need to put more effort into listening for more than one possibility.
Edit: Aaaand two minutes later I made the same mistake. facepalm ;)
They're interchangeable, wherever you have אנחנו you can also use אנו - but bear in mind it's more formal. אנו isn't really used in spoken Hebrew.
You use את when the direct object is definite, i.e. אנחנו שותים את המיץ. (We drink the juice)