Also, I've noticed that when I type, not only do some things get underlined in red (I think it's for misspelling), but also in blue. Any idea what that means?

Red is a word that doesn't exist in the keyboard's dictionary (and likely a misspelling, but it sometimes doesn't have everything). Blue is a grammar check, and it's letting you know that your grammar might be incorrect (missing a word, verb doesn't agree with the subject, wrong word chosen, etc.). It's not perfect, but it may help you find mistakes you didn't intend.

I don't know what the green dot means. Sorry.