I just noticed that my HeliBoard icon in the list of apps has a green dot to the left of the name below the icon itself. I have no idea what it means -- it seems to be different form the privacy green dot you may get in the top notification area.
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?
Depending on your phone / android version / launcher this cab mean different things I guess.
On my phone (MIUI) a dot like that means this is a new app, after you launch it a few times using that icon (using icon, not by other means like jumping into app from a notification or via opening a link) that dot disappears.
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.
noticed the green dot as well and panicked - first few search results said that's an indicator someone's recording, either via mic or camera; checked the permissions log, no help there. haven't seen it after that.