It has 3 pre-installed fans, each with a molex(?) connector that connects to the PSU. There is no adapter or instructions that allows me to connect it to my Motherboard (Asrock ext 3 gen 3).
The fans are a bit loud running at 100% all the time, I've unplugged the big 23cm fan on the side to silence it a bit. If my mobo (or I) could control the fans, it would make my system much more quiet when I'm doing work.
Is there some kind of converter/ adapter/ extender chord that will let me plug in the molex and then plug into the tiny 3 pin connectors on my mobo?
Usually the mobo one has one plug that can control fan speed and that goes on your CPU fan. If you want to be able to control all the fans in your system you'll need a fan controller, something like this:
That adapter you linked from eBay Australia would allow you to connect one of your fans to a mobo fan output port. (So, 3 adapters for 3 fans.) However, the degree of control you can get may be limited.
Your mobo has 2 CPU_FAN connectors - one 3-pin and one 4-pin - and these can ONLY be used for the CPU cooling fan. The manual appears to say that these only work in 4-pin fan mode. That is, the 4-pin output will control the speed of a 4-pin fan. BUT that same port will only operate a 3-pin CPU cooler fan at full speed. If you plug such a fan into the 3-pin CPU_FAN port, it is not clear but the implication seems to be that it, also, can only operate that fan at full speed.
Now to the case fans, which is what you asked. First, recognized that your fans operate similar to 3-pin fans because their speed can only be controlled by varying the voltage supplied to them (0 to 12 VDC). They do not have the extra connection line and special internal chip of a 4-pin fan. Moreover, they do not have the third line that takes the fan's speed signal back to the mobo, so you will never be able to see the speed of any of these fans.
Your mobo has three case fan ports, marked as CHA_FANn, from 1 to 3. Configuring them in BIOS is outlined on p. 70 of your manual. CHA_FAN1 is a 4-pin port, and apparently operates only in 4-pin mode. That is to say, it can control the speed of a 4-pin fan. But for a 3-pin fan, it can only run that at full speed or at some fixed speed set manually in BIOS. That is how it can operate one of your fans if used with an adapter.
Both the CHA_FAN2 and CHA_FAN3 ports are 3-pin connectors and appear to operate similar to each other. They do NOT have any automatic speed control function. Each can be set to full on, or to some manually-set reduced speed (set in BIOS).
So, you can use your 3 mobo CHA_FANn ports to connect your case fans via adapters, and you can use manual settings in BIOS to set those case fan speeds. You cannot display any fan speeds (because the fans don't generate any speed signal to measure). This virtually duplicates what you could achieve with a fan controller module mounted in the case front. The difference is that a controller module would provide front knobs to set the fan speeds, whereas the mobo-based ports appear to require that you set those fan speeds in BIOS during a reboot. There MAY be another way. Some CD's with mobos contain a utility you can run in Windows that allows you to check and set fan speeds or voltages. Your mobo's manual indicates yours has utilities on the CD, but gives no details. So I don't know whether you have a utility on there that would allow you to set fan speeds manually within Windows, or whether you would be forced to reboot through the BIOS Setup screens to set fan speeds.