What are all the two letter words that have apostrophes in the middle of them? i.e. I'm I'd?

They are so called "contractions".

I, as the first person singular, is the person and subject of those sentences. The English language allows several contractions with some words. Mostly "not", "be", "have/had" and "will/would".

I'm is a contraction of I am, while I'd is a contraction of either I had or I would - this is depending on the context of a phrase.

Others of this kind would be "I'll" for I will, "I've" for I have.

"Not" only contracts with modal/auxiliary , meaning: have - haven't/hasn't or hadn't be - aren't/isn't (But always I am not or I'm not), wasn't, weren't can - can't, couldn't must - mustn't shall - shouldn't will - won't, wouldn't

Contractions are used in speech and also informal writing. So they have to be avoided in formal writing (e.g. application letters, protocols etc. Except it's a quote of what was spoken.)