Oh well. Good example - everbody makes the occasional mistake - that simply makes it even more important, to correct as many as you can.
The latter point might seem strange, but it obviously isn't incorrect. I often use 'it is', to be honest, because I've never liked 'it's' - the rules of when to use an apostrophe in it seem a bit of a minefield.
Agree with you. Mistakes are acceptable, but blatant ignorance of the correct their, there or they're, for example, is annoying.
Regarding the second point, 'its' is possessive and 'it's' is a contraction of it is. There are no other rules.