The pandas library has a guide on how to work with styles, but warn that it is a new feature, implemented from version 0.17.1.
In this link I provided you can find snippets of code to paint, create graphics, change colors of the contents of cells, among others.
Change color of column names: I believe it is not possible.
Fix the size of cells: believe that not, however, found this topic teaching an alternative to changing the size of cells using (more or less) the pandas library.
Add an image: is possible using xlsxwriter as shown in this topic.
Besides pandas library, I know two other libraries that allow you to manipulate spreadsheets:
And the library openpyxl, that also has a topic just to talk about how to work with pandas and a topic teaching a little about how to work with styles.
In addition to these libraries, I leave this link that I found extremely informative:
Improving Pandas Excel Output.