As stated in the comment these are creative ways to say goodbye. The rhyme often matters more than the meaning.
Catch you on the rebound
In ball playing the ball thrown may bounce back to the thrower or the opponent. Catching you! on the rebound means "I will see you on your return or when we meet again."
To the winch wench
I can only interpolate this as a request for me or you to return to work or a task at hand. The winch being the machine that needs cranking and the wench an endearing description of the one to do the cranking.
Take care, butterfly
Butterfly would be the one I was saying goodbye to. Take care is a common salutation.
Blow a kiss, Goldfish
Never heard this one but again the I am telling someone I know well enough to call goldfish goodbye.
Don't get attacked by a bear, it's night-time!
You got me with this one.
Saying hello or goodbye hardly matters here since it is good advice at night.
Once more unto the breach, dear friends!
Certainly Shakespeare. I think Henry the Fifth, telling his remaining soldiers that they have to go back and fight again. A very tough sell but with amazing results; real history.
Time to scoot, little newt.
I'm telling someone to get going, scoot being a verb.
Forever and forever farewell. If we do meet again, we'll smile indeed. If not, 'tis true parting was well made (I just don't understand the meaning of the last sentence in this one)
Rephrasing with apologies to Oxford "Goodbye. I don't expect to see you ever again. If We do meet again that will be great. If we don't then it's important that we say goodbye properly or; it is true/important that parting/saying goodbye is done properly." I'm sure the iambic pentameter app will do wonders with this.