There was grass hay to cut and a few head of livestock including horses, cows and llamas.

There was grass hay to cut and a few head of livestock including horses, cows and llamas.

Don't say 'grass hay to cut'. Say either 'grass to cut' or 'hay to make'. The latter sounds more like the way a farmer would speak.

I'd prefer to say There was hay to make and a few head of livestock, including horses, cows and llamas because the last phrase sounds like a minor, parenthetical kind of afterthought.

I'd also consider adding a comma, perhaps, after 'cut',because the structure of the two phrases is not parallel.

Yes, a comma after livestock, because the added information is not definitive. 'Grass hay' does not make sense to me-- use one word or the other.
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You place a comma before "including" only when the "including" phrase is non-essential, meaning it is just added information and is not necessary to clearly understand the meaning of the sentence. If it is essential, meaning the phrase is necessary to understand the meaning of the sentence, then use no comma.

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Grass hay makes perfect sense as there are different kinds of hay, such as alfalfa hay, grass hay, mixed hay, etc. I live on a ranch and we say "grass hay" all the time to distinguish it from the "alfalfa hay"
I agree because it is really a reduced for of a non-restrictive relative clause: , which includes.
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Thank you for your answer! Based on what you said, in the sentence below there should be no comma before 'include', did I understood correctly?

"False names that students have used when substitute teachers were in class include, Sandy Beech, Frank Furter, and Ben Dover."

Thank you in advance.