99.9% yes. Obviously, your USB host must support USB keyboard/mouse input. If you are not sure, check with generic USB keyboard/mouse first
It may happen that support for USB input devices is limited, for example: console allows to use USB keyboard in system menu and chat but as a game controller. Some platforms may not support (or only partially) functionality like multimedia keys (consumer control interface).
If your USB host does not support composite USB devices (both keyboard and mouse interfaces in one USB device) it is possible to change InputStick USB configuration, for example to set it as USB keyboard only (mouse functionality will be disabled in such case):
InputStickUtility -> My devices -> more -> Security (padlock icon) -> Connect -> USB Config.
No. Your OS should use generic drivers for USB HID input devices. Usually no configuration is required, just like in case of generic USB keyboard/mouse. Your PC is not aware of Bluetooth interface, so no there is no need for any Bluetooth-related configuration on your PC.
OS X will ask you to "press key next to left shift" in order to identify keyboard layout, when InputStick is plugged in for the very first time. You can do this using USBRemote application
You can configure standard keyboard/mouse options: repeat delay, repeat rate, sensitivity - just like in case of physical keyboard/mouse devices.
Note: always make sure that keyboard layout set in InputStick-compatible applications is the same as used by your PC.
Yes, you can use InputStick simultaneously with other devices like BT headsets, BT keyboards etc. Depending on your hardware, you may experience some performance drop: increased latency, slower typing rate.