Translation:You are all busy.
I don't think that that gets across the full meaning though. It should rather be ‘Y'all are all busy.’ or ‘All y'all are busy.’: not only is there more than one of you (indicated in Chinese by ‘们’ and in southern U.S. English by the suffix ‘'all’) but also none of you is an exception (indicated in Chinese by ‘都’ and in English by the separate word ‘all’).
In the textbook 'Modern Mandarin Chinese Grammar' they are translating 很 hěn as 'very' in the sentence. 他们都很忙 Tāmen dōu hěn máng. They are all very busy. 她少她今天很忙. Tā shǎo tā jīntiān hěn máng. She said she is very busy today. But actually it should not be translated as 'very' according to this explanation:
The basic formula for Noun + “is” + Adjective in Chinese: Noun + 很 + Adjective.
This is a great guide for those struggling to known when to use shi and when to use hen. https://www.fluentu.com/blog/chinese/2015/07/09/shi-chinese/
很 is a bit of an odd character in that it does mean very but it is also most often used simply as what they called in my high school a 'descriptive particle', basically meaning that before an adjective, to indicate that it was as such, you'd place that character. I don't know if there is really an equivalent in English so I can't really compare it to anything but I guess you could think of it as a grammar equivalent of how you might place a dollar sign before a number to indicate it being a price, e.g. $9. So to indicate that 忙 is an adjective you place 很, the 'descriptive particle', before it to make 很忙. [NB: I'm only a learner myself so anyone feel free to correct or adjust my reply if at all incorrect! :) ]
No. You can't always translate the English word to be to the Chinese word 是/shì. More often the word 很/hěn is used to connect the subject 你们/nǐmen (you) to the adjective 忙/máng (busy). Note that 很/hěn can sometimes mean very, but often it does not, like in this sentence.
你们 is plural and "you" is ambiguous, so "you" should be accepted alongside "you guys" because of the ambiguity, especially since the sentence already indicates plural "you" with the "all". I also acknowledge that English is a dumb language for not having a specifically plural form of "you". (When learning other languages, I have resorted to "youse" for clarity).