You didn't say you had iPad Mini 4. You said iPad Mini. Yes, a Mini 4 as long as it has iPadOS 13.4 or higher can use a mouse.
As to putting your mouse in pairing mode, you need to use the directions Logitech provided with the mouse to put it in pairing mode. If you don't have the directions, go to Logitech.com and look up the user manual for the mouse you own. Typically however underneath the mouse is a button you push to put it in pairing mode. If the mouse is already paired to another device, make sure that device is turned off or it won't go into pairing mode, unless the mouse provides for pairing with multiple devices. I have a Logitech MX Master mouse, which can be paired with 3 devices and can be moved easily between the devices by a tap of a button.
A final note: Since iPadOS 13.4 you may find scrolling on a 3rd party mouse is not very smooth or in some cases won't scroll at all. Logitech seems to work pretty well with iPad. Some other mice, not as well.