Learn English – Difference between “both ways” and “in both ways”

Just to put Davo's answer in as an answer, with a little more explanation...

In terms of the most essential meaning in this context, "in" and "with" have the same meaning. They both introduce adverbials indicating what it took to do what was done. "He broke the thick sheet of glass" stands as a sentence on its own, but is modified by the adverbial of manner "in one hit" or "with one hit". Both "in" and "with" can have other meanings, but here they introduce the same sort of adverbial. Adverbials of manner tell you how or in what way something is done.

However, as Davo notes, they carry different shades of meaning. "With" is more neutral than "in", as with would be more likely to be used if there is no surprise, and in makes it seem more remarkable. You can also indicate that you consider it remarkable by adding the word "just" - "in just one hit".

There isn't much of a difference here. In sentence B you're using the sentence structure
{Do something} for {Reason}. Examples include:

• "Go to New Zealand for business"
• "Go home for your mother's birthday"
• "Read a book for fun"

Sentence A uses a specific kind of English idiomatic phrase {Go somewhere} on {type of time}. By 'type of time' I usually mean something like "business" or "vacation". Examples include:

• "Go to New Zealand on business"
• "Go to Florida on vacation"
• "Visit Australia on holiday"

but not

• "Go to New Zealand on February"

If you're ever unsure whether to use "on" or "for" in that type of sentence, "for" almost always works, and "on" is only correct for a specific few cases. For example, you could say "Go to New Zealand for February" and that would mean you were spending the entire month in New Zealand.