"It's up to you!"
Haha, I am not sure. Afterall I am not native English speaker and I am afraid I would have misinterpreted some meaning. But it should be very close if not identical.
"At your convenience" would mostly apply to a time frame; "whenever it's convenient for you" where as "随便你" covers all kinds of decisions; which movie do you wanna see? 随便你. What color should the bride's maid's dresses be? 随便你.
I am glad that you haven't.
Have Duo even explained it? Usually "随便你!" is not a friendly comment. When you don't agree with a person's idea or follow his advice, that person would throw "随便你!" at you, which means "It's up to you! I don't care!"
In English, "it's up to you" and "I don't care" are very different. "I don't care" is quite rude but that's not the case at all for "It's up to you", which could even be regarded as pretty friendly.
Just not to sound misleading, if said nicely the Chinese meaning can be positive too.
e.g. A salesman saying loudly.
二十块一个! 什么都是二十块! 随便你! 快来挑!
Twenty bucks each! Everything is twenty bucks! It's up to you! Come quick and choose it!
But I suppose it's probably not something that would've been learned at this point in the course.
This is a rather unnatural English translation for this, imo. I've learned 随便 in my courses before, but translating it this way is a little opaque to me.
No. 你随便 is not an equivalent.
We can say 随你便! as an alternative, but not 你随便.
你随便, not with an exclamation mark, can be used when we receive a guest, but leave him/her doing whatever he/she likes, e.g. someone walking into your bookshop to find books, a schoolmate coming to work on your computer, etc. So it's pretty much like "Please feel free."
随便你 and 你随便 may not be equivalent in Chinese, but given the definition you describe, they both sound like they could be translated to the given English translation -- the English translation given is very vague, imo.
How am I supposed to know whether the speaker is being polite? I put 宿便您 and it was marked as incorrect! REPORTED...