If auto-ripple is something you toggle often, then I suggest you use a keyboard shortcut instead of pressing the button each time. I believe it’s Ctrl+L by default, but you can change the keybind in Options -> Customize Keyboard and search for “AutoRipple” in the top bar. Select Options.DoAutoRipple, click inside the shortcut keys field and set it to anything you like. It will show potential conflicts at the bottom.
You can also manually ripple by pressing F after making an edit (F for affected tracks, Ctrl + F for all affected, Ctrl+Shift+F for all).
As far as moving the whole timeline and/or the attached buttons – I know you can move them to the top of the window instead of having it at the bottom (Options -> Preferences -> Display), but not to the sides. Seems that those buttons are attached and the only way to see more of them is by shrinking the track panel all the way to the left.
However, if you’re set on using the mouse for this function toggle you can also do it via Options -> Ripple -> Auto Ripple