Would someone please tell me when it was that the apostrophe was introduced to the English language, and what the circumstances were?

The apostrophe denotes a letter left out to create an abbreviation. In the olden days, if you had wanted to say mibmob's book you would have used the old genitive mibmobes. The apostrophe shows the contraction that we have now. It is a sadly lacking commodity where it is needed and overused where it is not ("ripe apple's for sale")

It is named after the Greek word apostrophos "of turning away, or elision". So apostrophe was the elision of a letter or letters in a word. That usage dates in writing from about 1611. Interestingly, it was earlier that the punctuation mark apostrophe came to be so named as it represented the letters elided. Shakespeare first uses the word in this sense in 1588 in Love's Labour Lost. It is possible that the word for the process preceded the word for the punctuation mark but didn't make it into the written record. English took the word from French apostrophe, which came from the Greek via Latin apostrophus.
The apostrophe used to denote possession is the same as the one described above that is used to denote a missing letter or letters. The apostrophe in a word like fox's represents what was originally an e as in foxes. So, before the apostrophe was adopted, a possessive was formed just like a plural: "Look at the foxes beautiful tail." The use of the apostrophe for the e was then expanded to all words in order to denote possession. This became widespread after 1725.
It was probably around that time that the first contractions appeared with an apostrophe. Prior to that time, contractions existed, but the missing letter or letters were not identified with a punctuation mark. For example, as early as 1420 we have wynnot for will not, cant (1706) for can not/cannot, and dont (1670) for do not. Then we find won't in 1667, can't in 1741, and don't in 1672.

Why won't ?

Cannot / can't
Do not / don't
Fair enough !

Will not = Won't ???
Why not willn't ?

If won't is a "new word", why not just WONT.
What letter is missing ?

Charlotte Bronte used it in Shirley in 1849 in order to represent local Yorkshire speech: "That willn't wash, Miss". It turns up also in Mary Barton by Elizabeth Gaskell: "No, indeed I willn't tell, come what may". So why the o in the contraction when it should be i? The answer lies in the irregularity of the verb will: it varied a great deal in different places and at different times. Though the present tense was often wil or wille, there was a period when it appeared as wol or wolle; this was especially common in the Midlands of England in the late medieval period, and may have been an unconscious imitation of the simple past tense, which was spelled and said with an o as standard. For some reason, though the present tense eventually standardised on will, the contraction of the negative settled down to be won't, using the vowel from the other form.

Older locals in this part of the world are sometimes given to using the word "cassn't" to mean cannot, as in "E cassn't do ort" meaning one is unable to do anything.

It's a beautiful dialect.