I have collected some English idioms starting with "Don't". Are there any further that you can suggest me?(That start with "don't) or is any reliable site that gathered these idioms?
It may have been used in a song or two, but I can't find many examples of 'go/come between the bark and the tree' on the ineternet, so it doesn't seem to be commonly used. Like Roman, I have never come across it before,
There's is a bit of everything in the list. Your colleague is perhaps right about some of them.
They are not all used exclusively with "don't" either.
To rock the boat, to wash one's dirty linen in public and to put the cart before the horse are definitely idiomatic.
#14 is not an idiom. Most of the others are proverbs and idioms. It all depends on whether the meaning can be determined only from the words themselves.
Don't let the bedbugs bite.
Don't hold your breath.
Don't burn your bridges.
Don't get mad; get even.
Don't get me wrong.
Don't get smart with me.
Don't give me any of your lip.