I found 2 different themes that i liked for my blog but each one has something the other doesn't have that I want. For instance, This Theme has those cool calender icons that I'd like to put on my other template I'm going to use. Is this something I can do or am I stuck with the way the other is designed? What exactly can be added to a Wordpress theme?
Yes you can do it, you can add any image, icon, text, or whatever to a wordpress theme, its like a normal site.
Most of it can be edited if you know what you're doing. If you don't get one that fits your needs best possible.
usually all wp themes can be edited. but some coders lock footer.php with encryption because they want to protect their sponsored links on it. so theme users cannot edit file footer.php. the rest files, you can edit as you like. -cypher.