Welcome to the forums
1) I use two monitors for my usual workflow, and games that rely on moving the mouse cursor around on screen should really capture the mouse on the game's monitor. As it is now, clicking on my secondary monitor minimizes the game.
I'm sorry, but it's a Unity engine game and Unity doesn't let us change the mouse position. Including snapping it to the window.
2) I have a Saitek x52Pro I use for flight sims and the like, and because I leave it plugged in and typically the throttle and sliders are usually set all the way to one side, it is necessary that games that are set to be using only Keyboard and Mouse inputs specifically ignore inputs from other game controller devices. Currently I start the game ducking continuously, and at one point on the second screen I mysteriously started creating wooden platforms repeatedly for no reason.
The default controls (keyboard+mouse) are set to recognize all forms of input so that someone starting new as a gamepad user doesn't have to switch to another setting to get their input device working at all.
If you would like your gamepad to not do anything in the game but don't want to unplug it or otherwise position it so it does not cause unintentional inputs, you may edit the controls (you can get to that from the Settings window) so that none of them have anything bound to a joystick button or axis
Thanks for reading and good luck with your product!
Thank you for the feedback, I hope you enjoy the game