For the first one, I will give it a shot again. For the second one, yes, that’s where I expect to see the Magic Mouse.
Make sure you do it from Accessibility, as, in my experience, it will not show up from Settings → Bluetooth.
The pairing process seems to be a bit buggy but once it's paired it works well.
In trying to help with your issue, I unpaired mine on purpose and then struggled a little to get it to pair again (first time I tried, it just worked, I guess I have been lucky =) ).
In the end, I think I found a way that seems to works consistently.
1) Unpair your Magic Mouse (1) from any other paired device and turn it OFF. Just to be safe, you can also turn OFF bluetooth on your Mac.
2) Enable AssistiveTouch on your iPad (Settings → Accessibility → Touch → AssistiveTouch → AssistiveTouch ON)
2) Now turn OFF your iPad.
3) Turn ON your iPad
4) Turn ON your Magic Mouse, make sure the green light is blinking
5) go to Settings → Accessibility → Touch → AssistiveTouch → Pointing Devices → Bluetooth devices
6) Wait a few seconds for your mouse name to show up on your iPad, then tap on it.
7) Input the pairing code (0000 worked for me).
8) Enjoy!