st got it, but my two cents/more info...
1. Mame does use the mouse buttons, but "sort of" not be default. First, mame defaults not to use the mouse (-mouse 0), so no inputs from the mouse are used. Okay, so you enable mice; mame input map defaults include the mouse buttons. "Include" is the word; there is no input in mame with only mouse buttons mapped to it and all inputs that a mouse button is mapped to also is mapped to keyboard (and joystick) buttons.
Example: player one button one has the following mapped by default: keyboard1 LCtrl, OR joy 1 button 1, OR mouse 1 button 1, OR lightgun 1 button 1. Notice the "OR"s; if any of these are pressed, mame sends the game that player 1 button 1 was pressed.
2. Yes. Any input* in mame can be remapped to any input device and button/key. Mame can map ORs like the example above, and ANDs (combos where all ANDed inputs need to be pressed at the same time), and NOTs (compare reset vs soft reset: the former is F3 + LShift, while the latter is F3 if and only if LShift is not pressed at same time). But you don't need to remap.
(* hardcoded debug inputs can't be remapped in software, but they are rare, and removed as the game is better emu'ed.)
So for mame you don't need mouse buttons. Windows, Front Ends, other emus, other games, other apps might, though, so look at them and see if any you're going to use needs it.