Your particular board has two 4-pin headers and three 3-pin headers.
And yes, you can mix/match fans and headers. Plugging a 4-pin fan into a 3-pin header just means the fan can't work in PWM mode. You can also plug a 3-pin fan into a 4-pin header. However if you do this, that fan will likely be set to full speed. This is because the mboard will try to control speed using the fourth PWM wire that the fan doesn't have. Read below to understand why.
Fan speed control is handled in two primary ways: you can either change the voltage to the fan or change how long the voltage is turned on. The first method is the oldest. Using resistor wires or fiddling with the 12V, 3.3V, and 5V lines on the mboard let you set a fan to run at 12V, 8.3V, 7V, 5V, or 3.3V.
However that was a static speed and it wouldn't change if you needed your fans to speed up or slow down. You also ran into problems with some fans that wouldn't run properly at lower voltages. Most fans can run at low voltages, but they require a higher voltage to get them started up first. You often hear every fan at maximum speed for the first second when you start a computer because it's getting everything spinning first before it lowers the voltage. So after-market fan controllers became popular because you could use a variable resistor to change the voltage to a fan, usually controlled by a manual dial on the front of a machine.
PWM stands for pulse width modulation which does something completely different. Instead of changing the voltage fed to the fan, it simply switches the power on and off very fast. This on/off signal is what gets sent over the fourth wire. This means the fan still gets the full 12V blast to get it spinning, but changin the voltage pulse also gives much finer control over how fast the fan spins. This is why it's popular for CPU cooler fans, because you get exactly the speed you need without any excess noise. Some third-party fan controllers can take in a PWM signal and then repeat that same signal to every fan on them. This lets your mboard's CPU fan controller work for all the fans in your system.
However PWM isn't quite as necessary as it used to be because most mboards now can dynamically change the voltage they send out over their 3-pin headers. If you check in your BIOS, you should see a fan control section that lets you set desired fan speeds and maximum temperatures. However, your board is a little old, so it might not have all the fine-control a current mboard would have.