Concerning mouse usage in the Geneve emulation:
The mouse is immediately active in the MAME emulation, but it may not be synchronized with the desktop pointer. I recommend to let the mouse be "captured" by running MAME with the flag "-mouse". In that case, your desktop mouse pointer is captured inside the emulation, and you have to stop MAME to get it back. (Remember this is possible without the mouse by switching to Partial mode with ScrollLock, then pressing ESC.)
If the mouse buttons do not work, you have to adjust the input source. Get into the OSD menu, select "Input (this machine)" and scroll to the section [root:colorbus:busmouse]. The mouse buttons should read like "Mouse B1" etc. If not, particularly when there are key names like LCONTROL, highlight the option, press DEL (→"None"), press Return (→"< >"), press the desired mouse button.
If "Mouse X 3 Analog" does not say "Mouse X", do the same here, i.e. remove the entry, press Return, and move the mouse horizontally. The same holds for the Y direction.
The thing about capturing is yet another problem with emulations. You may know tools like VirtualBox or VMWare which allow for seamless mouse integration. Please remember that you typically run a graphical operating system in that virtual environment with similar properties as your host system. In turn, MAME cannot know how to translate a desktop mouse movement into impulses that make the emulated mouse run at the same speed as the desktop mouse, since this is ultimately controlled by the TI or Geneve program running inside.