If you look under the Bundles
menu in TextMate there is a Python-specific sub-menu that exposes a bunch of helpful things like syntax checking, script debugging, insertion of oft used code blocks, manual look ups and so on. Most of them are bound to keyboard shortcuts (or can be bound if they are not).
Also, under the Bundles are sort of general-to-code or general-to-text-editing tasks in sub-menus.
You can set up templates for new file creation that let you start new files with all the little bits and pieces you like to see in new files (copyright notice, author, SCC tags, etc.) See the File -> New From Template -> Edit Templates...
menu option to do that. It ships with 4 Python templates already.
Finally, that browser is called the Project Drawer. View -> Show Project Drawer
to get it to show up. It'll only be available when the window you're viewing is a project window, not a single document window.