As long as there is a fuse or circuit breaker rated at 40 Amps or less installed between the battery pack and controller then 12 AWG wire is a safe size to use.
If the battery pack has two red and two black wires then two of them could be jumper wires and the other two output wires, or all four wires could be output wires, so that would need to be determined before making the connections. If you could attach a photo of the battery pack then we would be glad to take a look at it and let you know.
The battery pack manufacturer may have run out of thick gauge output wire when they built that battery pack so they used two thinner gauge wires instead. Both of the battery pack's red wires and both of the battery pack's black wires will need to be attached to the new connector.
I agree that the XT90 terminal is not going to be big enough for the two 12 gauge wires. Only one fuse is needed in the circuit then a second fuse is not necessary.
The fuse would not be located up near the handlebars like that. It would be in the battery box that is under the footplate.
The white plastic trunking is too narrow to contain a fuse holder and the yellow junction block only connects the wire terminals together and does not contain a fuse.
There are no electric scooters which do not have fuses or circuit breakers. On the type of scooter that you have the fuse is usually located on one of the battery pack jumper wires or on the battery pack output wires.