So my question is, does 350 mA~2000 mA mean the motherboard doesn't support a current smaller than 350 mA? Would it work?
The other thing is that my motherboard only has 3-pin headers for chassis fans, and the fan has a 4-pin connector.
I tested the fan, and it seems to be working, but I wanted to know if it can damage the motherboard or something. If not, what is the 4th pin in the fan connector for? I just ignored it and connected the 3 others.
Also, I've used the CHA_FAN1 header for the fan, instead of the PWR_FAN header. What's the difference?
No difference. The cpu fan should be connected at all times. The fan you selected should work fine in either connector. Check the hardware monitor section of the bios for settings. If you want quiet, drop the numerical setting or max % fan speed and increase the trigger temp to 50 celcius. I use 12.5% for my fan setting; this may also work for your new fan. My cpu fan runs at around 1500 rpm in the winter; in the summer I bump it up to 2500 rpm.
No. Any small 4 pin connector that fits the pwr or cha_fan connections won't harm the board. I don't use the 4 pin direct power supply lead; can't control the fan speed using this connector, and I prefer quiet over lower temps.