Additionally, if I want to plug the fan into a motherboard header, can or should I use the adapters as well?
The supplied LNA adapter and ULNA are simple resistor cables. The LNA reduces the voltage to the fan from 12V to around 9V and the ULNA to something like 7V. So used individually they give a choice of two fixed fan speeds of about 900 or 750 rpm.
The normal alternative to the adapters is to set the Silent profile in the BIOS. For a chassis fan header on an Asus motherboard this will give thermal control equivalent to around the 7V to 12V range. With the NF-P14 this would be a rpm range of 720 to 1230 (using the figures from the SPCR review of the Noctua NH-D14 cooler
). In other words under idle conditions you should see around 700-800 rpm, and only under load and/or higher ambient temperatures would the fan speed increase.
You can of course put one of the adapters between the fan and the motherboard header. But instead of say 7V to 12V range it is going to be a lower voltage at both ends. So a lower minimum fan speed but equally it will reduce the maximum speed as well. The potential problem as always with 3 pin fans is that it may reduce the voltage to less than what the fan needs to start. It it easy to check that by rebooting the system and observing whether the fans run.
I tried attaching with the ULNA and Asus's UEFI monitor showed a really low RPM of ~300 I think in red text. Is the red text due to the voltage being too low or perhaps it's an indication that I plugged in a 3-pin fan into a 4-pin header?
The Asus BIOS has a minimum fan speed setting for both the CPU and chassis fan headers, you need to set this to Ignore which will remove the red text.