Learn English – “Filled in for someone” meaning

In general it means everybody, without exception

In this case They slew them to a man is They killed everybody, without exception.

Note that you cannot, as in the question title, "slay somebody to a man" -- you can only "do something to a group of people to a man".

OED1 says

Indicating a limit or point attained in degree or amount, or in division or analysis, and thus expressing degree of completeness or exactitude: As far as; to the point of; down to (an ultimate element or item) to the last man; {to a man} (including every man, without exception).

And provides some examples

• 1618 Bolton Florus (1636) 149 They might have had the killing of all his Army to a man.
• 1867 Froude Short Stud., Erasm. & Luther ii. 99 The bishops were hostile to a man.

It's not all nasty though, to a man is often used when everyone agrees perhaps in a sentence like this.

After a long meeting they agreed, to a man, to go back to work.

Depending on what your are reading, you might also find every man Jack [of them] as an idiom that means the same thing: every single one [of them] (OED1 again)

• 1840 Dickens Barn. Rudge xxxix, ‘Every one of 'em,’ replied Dennis, ‘Every man Jack’.
• 1859 G. W. Dasent Pop. Tales Norse 347 Every man Jack of them are so sound asleep.

Shed as a noun almost always means "a storage building".

Shed as a verb almost always means "losing skin or something covering oneself".

If an article (a/an, the) precedes a word, that strongly indicates it's a noun. So a shed is a noun.

You might see a shedding which would almost always be the gerund/participle form of the verb to shed. This can mean "an event where shedding took place" or "item produced by the act of shedding."

I suppose there may be a tiny chance that to shed means "to put in a shed" but I can't recall ever actually hearing/reading that.