How can I set a shortcut to close the window of TotalTerminal
I think my answer to your other question largely applies here too, but to specifically answer this:

If you tick the checkbox in the TotalTerminal preferences to show icon in Status Menu,  it should allow you to ⌘-w and reactivate without having to relaunch. You might also be running into issues with it seemingly not reactivating due to conflicting shortcuts in various applications, in which case I recommend trying a modifier-only "hotkey". ⌥ + ⌥ seems to work well.