Suggested answer:
(1) Examples of the three expressions from the corpus:
A study of the egg and bacon and tomatoes ...
It's the worst you can imagine, down and out in Wigan.
'Yes,' thought Fleury, 'she's going at it hammer and tongs for his benefit!'

Only the expression egg* and bacon occurs with the items in a different order; this order is in fact the preferred one in the corpus:
Nothing in the world tastes better than bacon and eggs cooked on a wood fire...

(2) Only down and out occurs with both a literal and an idiomatic meaning. Literal:
He had pushed the thought down and out of sight, ...

Idiomatic (="without any means of livelihood / empoverished"):
It's the worst you can imagine, down and out in Wigan.

Hammer and tongs only occurs with an idiomatic meaning (="to do something, especially to argue, with a lot of energy or violence") (see the example above).

(3) Kick the bucket clearly occurs with a literal mening in the following example from the corpus:
Brigg shuffled in, still kicking the bucket with the side of his boot...

(4) The two expressions do NOT have the same idiomatic meaning. Beat about the bush has the meaning of "avoid the point at issue", e.g.:
...lot of time is wasted by not speaking the truth - by beating about the bush instead of coming straight out with things.'

Kick the bucket means "to die", e.g.:
... and then my old woman kicked the bucket.

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