That’s right it’s the L1019 to Z916 motor cable adapter, they have two options you should need the L1019 female end and Z916 male end. That connection is on the bikes chainstay to verify before purchase.
I believe your controller/battery should have a yellow XT60 connector I’m not sure though, it’s possible it has an XT90 or Anderson plug all of which are cheap adapters and available with fast shipping on Amazon and eBay. You could open the controller compartment and pull it out to check, if you plan to unplug anything take the battery out first and hold the display power button down for ten seconds to avoid being shocked. You may see the display light up for a moment dispensing the remaining power in the cables then it’s safe to unplug. Their silver KT controllers have XT90’s.
You could use the 25a or 30a controller no problem, if there’s more than enough room for it I recommend the larger ones at least 30 amps to make the upgrade worthwhile. It will only have cooler operation and can easily program it to lower amps and it’s nice to have the option of more power if you ever need it. You can lower the amps as well as adjust the gradual smooth start in the LCD8H. They also have a black 35 amp KT controller made for Rad Rover upgrades that will work with all this, the difference is this one has a yellow three pin throttle but a proprietary two pin battery connector. They have many adapters for that battery connector. If you use that controller check that it’s the same throttle male/female ends that are needed.
Your hydraulic brake levers have built in motor cut off for safety, the controller may be plug and play but I’m not sure. If not electrobikeworld sells ones that do made by JuinTech it’s an easy swap. For brake light/turn signals the KT controllers have the connections and ability check with electrobikeworld if they match they have great service. Example of separate KT brake/turn signal kit: