In a theme upgrade all the theme files are overwritten. This includes any images uploaded to the
themes images folder and subfolders such as header images, logo, and favicon so you will have to reupload them. There has always been a way to set the path for the logo and favicon to wherever you want with ../ code. With version 3.7.11 you can now use the same ../ code to set a path to the header images as well that is outside the theme folder. You can read about how to do that in
this thread.
All of the theme settings such as what is in CSS Inserts are stored in the database so will be preserved.