XBox 360 Controller Issue

Hi , I managed to get a game for related toddlers that was called "Paw Patrol The Movie" , the game surprisingly came set to work only with controller and my trials to switch it to work with keyboard failed . Now this is still quite unrelated to my questions .

So I dug out an old XBox 360 Controller to use it with the game , it was Bluetooth wireless version and was connected and tested to work just fine , then came a moment of truth , when I ran the game I was faced to need to click a Hamburger button (Menu button for Windows world) on controller , the controller however had no button similar to that and non of the buttons could trigger a response from game , after deep search I realize such button exists on controller Xbox One and above line of controllers .

So here are my actual questions :

1 - Is there a known way to map or use such a button on the XBox 360 Controller ?

2 - I researched my options on buying an XBox One Controller only to find its an entirely different world , now it does not use Bluetooth and if I want to hook it up to the PC I need to use a converter and wire it so the PC recognize it as a USB device , so seriously is that it ? I spend so much on a controller only to use it as wired ? There is no wireless version that works with PC ?

3 - There is a known gamepad mapper that can actually map any gamepad into an XBox 360 /controller for PC , is there another known to do the same job but as XBox One ?

1. You could get a cheap Switch 3rd party controller. However mine Wireless does not work but plugging in via usb-c to USB it works like any native 360 controller. It is called a N-SL controller. It is a knock-off but it works great as a plugged in controller.

2.AntiMicroX you can ping any button to controller but their is a slight delay.

3. X360ce is an alternative and has pin-point accuracy but kind of annoying to setup. You might have to disable a couple of bypasses in order to get it to function.

4. The original X-box controllers did work back on Vista ( I believe ) but now they do not. You have a dedicated converter, even a

X-box -> PSX -> PC

or

X-box -> GCN -> USB ( WiiU converter ) -> PC

I doubt there are any dedicated X-box to PC converters out there. Maybe they are? IDK.