Hello Mahlon,
Here's my answer. The icon with green tick means that the post is answered, this icon generally appears when the person who is replying to the post mark it as answer. So when someone reply to any post on the forums and they think it is the final solution to a problem and no futher actions required they can mark that post as answer. You can do this after you post your reply, you will see Mark as Answer button, click on this button and it will mark that post as answered.
The next icon is with red Question mark, it appears when someone ask question or post on forum and they select not answered on the dropdown menu.
The Icons on the left hand side basically shows if the post is read or unread.
It means post is New or Unread.
It means post is Read.
Hope this helps!
-Inder