Mobo fan headers each have three main functions: (a) supply power to the fan motor; (b) control the fan's speed - usually 4 options, with automatic control as default based on a relevant temperature sensor; (c) detection of FAILURE of the fan - may be triggered by NO fan speed signal, or by a speed less than some alarm limit.
With those mobo headers and your equipment, I suggest these connections.
Plug the PUMP unit into the AIO_PUMP header. This header will always supply the pump with full 12 VDC power so it can run full speed as designed. Presumably it also will monitor it for no pump speed signal indicating failure. In an AIO system, the most critical component to monitor for failure is the pump.
Plug the three rad fans into the CPU_FAN header. This is the only header that uses as its guide the temperature inside the CPU chip, which is the only reasonable guide for cooling that chip. On most mobos, this header gets special attention on the question of failure of its fan, because the CPU chip is so critical and so expensive if it does NOT get cooled. The fact you have nothing plugged in there now is exactly why it will not let you boot up normally - it believes that the cooling device you have for your CPU is NOT working and will not let you risk overheating it. Now, since your system did not come with a three-output Splitter for those fans and you have only a 2-output one lying around, you need another. If you can get one easily, get a Splitter with three outputs. But you may find it easier and quicker to get TWO of those common 2-output Splitters. Then make a "stack" by plugging two of them into the outputs of the third, That gets you four outputs from a single mobo header. Connect that to your CPU_FAN header, and connect your three rad fans to its outputs.
Now, just a note to remind you. Any mobo header can deal with the speed signal of only ONE fan coming back to it. So when you use a Splitter, it will return to the host header only ONE of its fans' speeds while the others are ignored. This has NO impact on ability to control speed, but it does impact Failure detection - the header cannot detect a bad speed signal it never gets! So in such a case it is up to you to check from time to time to ensure that all three of those rad fans are working. And here's a further note because of this if you use my "stack" concept. The most common way for a Splitter to do this is NOT to have Pin #3 on any output that is NOT sending its speed back. So look at your 2-output Splitters, and the one output that has all FOUR of its pins CAN send back the fan's signal. Identify which if the two outputs of the first Splitter that is. Then on the second Splitter that you plug into that output, identify the one that DOES have all four. Just make sure that, of the four outputs of your "stack", the second-level one with its four pins DOES have one fan plugged into it so that that signal WILL get back to the CPU_FAN header and keep it happy.
Finally, we're down to your exhaust fan. It can go to a mobo CHA_FAN header, since it will use for its guidance the temp sensor on the mobo, indicative of general case heat and cooling needs.
With what you have I suspect you will have enough cooling. The CPU in particular should be well cooled by that system. If you feel that the case itself and some mobo components might need more cooling, you could add one more exhasut fan - I'd guess you could mount one ot two at the top. Connect that to a CHA_FAN header also. In the fan configuration screens (see your manual p. 3-7), configure all the case fans the same. One small detail: I believe all your fans (rad and case) are of the 4-pin design, so set all your fan headers to use PWM Mode (top right of the configuration screen for each).