Re: It's and it's
You are absolutely correct that apostrophe-s is used to indicate possession. The confusion is between the contraction and possession, that the rule of thumb I was taught helps.
The additional source of confusion is that " its " seem strange not to have an apostrophe, even though it indicates possession. The 'explanation', more of another rule of thumb (isn't English marvelous?): possessive pronouns do not use an apostrophe, witness his (his true spots are showing), or hers (those spots are hers), and theirs (the spots are theirs).
And let's not even get started on all the other forms of contractions, like I'd, haven't, could've (the mother of could of), etc..
Some languages are so orderly that one can easily remember the small number of exceptions to the rules. English is one where the number of exceptions just might exceed the number of rules.