Error 30 is usually communications between display and controller. It happens if the controller isn't being turned on with the display, or when the display and controller aren't compatible (not from the same "kit", etc), or when the controller is damaged, or when the wiring between display and controller is damaged or wrong.
In most of those cases the controller isn't operational, so it won't run the motor.
There are additional causes for a motor to not spin when commanded, such as battery being too low a voltage so it's below the controller's LVC, so things turn on but won't power a motor in order to protect the battery.
If hall sensors are "bypassed", they wouldn't be connected. Or, since the display can't talk to the controller to change or read settings, the controller setup software would have to show that it is set to sensorless mode, if it has such a mode and if it has computer or phone based setup software (most don't).
For wiring, I can't tell any of what you have connected where--pictures like that just aren't sufficient to tell that kind of thing, and there's no standardization for what wire or color connects to what other wire or color; these are specific to the specific devices and parts on each bike.
To show us what's wired where in a way that we can help you with, you'd need to draw up a wiring diagram (on paper or in the computer) by tracing out each wire and drawing what device it comes from and goes to, marking the colors used as well (it's ok if you don't know what things are called, as long as the drawing shows what they are so we can figure it out).
I'd recommend that in any case, so you have something to go on for troubleshooting now and in the future, but it's especially helpful when you get a system that presumably doesn't work and you have to figure out why it's not working, and the wiring has been modified in any way.
Since it's a Stealth Bomber you should be able to get info on what's on the bike and how it's connected from Stealthbikes in Austrailia--each bike is serialized so they could have records specific to each one. At the least you can find out what came on the bike, and get manuals and documentation for them. If any parts have been changed by the previous owner to something else, you'd have to find the manuals/etc for those from the manufacturers of those specific parts.
Battery "pop" at the connector (with an arc flash) is normal for any system that does not have a precharge or a switch to turn the battery off prior to connection, as a high current flows for an instant to charge the controller capacitors.
Your first goal in a situation like this is really going to have to be making sure the system is correctly wired, everywhere, for all wires to all parts of the bike. Easiest way is to start with just the battery and controller and display, nothing else. Once those are working, you can then connect the motor and try a self-learn, if the controller has that function.
