FF7 is limited to by its input driver, that is based on Direct Input from DirectX5 1997. While this version did see improved support for controllers it does not support enough buttons or axis to read all the ones on a more modern controller like a ps3 or ps4 controller (iirc you can do this w/ ps2 only because you can toggle the axis mapping w/ the analog button). The ps4 controller has 13 axis d-pad x/y, L-Stick x/y R-Stick X/y trackpad X/Y L2,R2 and physical X/Y/Z and 14 buttons. When you computer uses them it will map them to various axis and button numbers for applications to use . FF7 can still only access, axis 0/1 and buttons 0-9. To Fix this I use an application like joy2key and just map keyboard inputs to the controller buttons externally of FF7, still not perfect but its much easier to map so i can switch between dpad and analog stick like i used to with a ps2 or ps1 dual shock but now over bluetooth.
3. See the ini config file for aali's driver in your install path.
4. Wanna skip the logos remove the movie files the game will fail to load them and move on