Is it possible to edit themes?

https://www.urbangiraffe.com/themes/guides

Is a great set of articles on breaking down the default theme and reconstructing it to your liking.
There are numerous articles in the codex on the topic as well
https://codex.www.ads-software.com/Main_Page

That section has some great content. But reading through it, I am still unable to find an answer to my particular problem. The problem is that the theme appears to be somehow locked. Here’s a screenshot of the message I get: https://colocationblog.com/images/screenshot.gif (look in the red circle).

I can’t access the graphic you are referring to, but if you mean that the bottom of the WordPress built-in Theme Editor has a line that says “If this file were writable you could edit it” or something like that, then you will have to change file permissions.

https://codex.www.ads-software.com/changing_file_permissions

And more specific information that will help you with your Theme changes and development:

https://codex.www.ads-software.com/WordPress_Lessons
https://codex.www.ads-software.com/Blog_Design_and_Layout
https://codex.www.ads-software.com/Templates
https://codex.www.ads-software.com/Stepping_Into_Template_Tags
https://codex.www.ads-software.com/Theme_Development
https://codex.www.ads-software.com/Using_Themes
https://codex.www.ads-software.com/Site_Architecture_1.5

Lorelle has touched on the permissions issue, and I’d add that though the theme editor feature is a good stop gap/quick fix editing option, for a more comprehensive tasks, such as you proposing (mashing 3 themes together), I would highly suggest editing your files with a text editor. I can’t speak for the Windoze platform, as I’m on a mac, using cyberduck for ftp (which then allows me to directly edit files) and smultron for the editing.
I’ve heard the apps filezilla and notepad plus thrown around the forums quite a bit, so perhaps a search for text editor would turn up one of the threads on the subject.

A good list of text editors is available here:

https://codex.www.ads-software.com/Glossary#Text_editor

[Microsoft Word is not a text editor.]