I presume the "3*3pin adapter" you speak of is what we call a SPLITTER that simply converts a single 3-pin mobo header into three 3-pin outputs. It has one arm to plug into the header, and three output arms with pins, and NO other connections. Is that right?
A Splitter simply connects all of its fans in parallel to the power supplied by the mobo header, so all fans get exactly the SAME feed. And all of that power can come only from the header. which has a limit on the max CURRENT it can supply, usually 1.0 A. Now it happens that most of the headers you are planning to use are designed for possible use for a pump, and hence with a higher max current output of 2.0 A per header. The 3-pin fans you have that came with the case all have a max current use of 0.30A, so three of those on one header comes to 0.9 A max, easily supplied from one header. For six fans total, one of the easiest arrangements is two Splitters to connect two groups of three fans each to two headers. For example, your existing three 14 cm 3-pin fans in one group, and the new three for the front in another group.
With 3-pin fans, the header alters the VOLTAGE sent out to change fan speeds. With a Splitter, all fans on that header get that same controlled voltage. If the fans are identical, all will run the same speed, from max down to the minimum they can run without stalling.
Four-pin fans (you don't have any) are controlled differently. They get a constant 12 VDC power supply, but they also receive the new PWM control signal from Pin #4. Inside the motor case there's a chip that uses that signal to control the fan sped. Because this method is different from how 3-pin fans are controlled, it is best not to mix the two fan designs on one header. In your case, though, it would be simple to place your three 3-pin fans on one header with a Splitter, and group the new three (of whichever design, 3-pin or 4-pin) on a second header using another Splitter.
For case ventilation fans, I suggest using the CHA_FAN/PUMP headers - you have three of those. Each of them can be configured in BIOS Setup to use the correct speed control method for the fans attached to it. This is the selection of MODE of the header - either DC Mode for 3-pin fans, or PWM Mode for 4-pin fans.
IF you decide to buy more 3-pin fans for the front, then the 3-pin Splitter type you have will be suitable. IF you decide to buy 4-pin fans for the front, then be sure to get a 4-pinSplitter. (In fact, a 4-pin Splitter can be used with 3-pin fans.) If you set up the fans in two groups on two headers as I suggest, then I recommend this set of configuration options in BIOS Setup. (You must configure each header separately.) See your manual, p. 79.
CHA_FAN/WP Switch to Fan
Control Mode to DC for 3-pin fans, PWM for 4-pin fans
Setting to Standard or Normal to have the pre-set automatic fan speed control system manage all these fan speeds according to temperatures measured on your mobo. The fans will run slow and quiet until your system heats up enough to need more cooling.
Temp Source to Motherboard, not the sensor inside the CPU chip
Doing this will give you automatic control of all the case fan speeds - quiet at low workloads, and increasing fan speeds only when the system actually needs that added cooling - and all done without your having to watch and manage them.
Just a note on a detail. Any fan header can work with the speed signal sent back to it from ONE fan only. So any Splitter will send back to its host header the speed of only ONE of its fans and ignore all its others. Youi will never "see" those "othrers". The most common way to do this is simply to include Pin #3 in ONE of the output arms, and omit that pin on all the other outputs.