This is the closest photo shoot I could get before the insect flies away or gets murdered by my hands.
Could anyone identify what insect is it?
Why does it attack my plant?
How to prevent that insects from coming to my house?
It looks and sounds like a fungus gnat. If that's all it is, adding a little food grade diatomaceous earth to your soil should keep them away.
I have a similar-looking critter in my house that isn't so bothered by diatomaceous earth, though, but it's not scared of humans, and doesn't fly away when startled (it just crawls around the houseplant soil, multiplies, and doesn't bother the plants; sometimes it's on fruit, but rarely). Our fly is also waterproof, like it's covered in wax or something, and it keeps regular fruit flies out of the house, it seems. It sounds like your fly is easily startled; so, I'm guessing the DE should work.
You might also, or alternatively, try cinnamon. I have a hunch it might work.
Improved ventilation, more light and poor conditions for fungus might also help.
Fungus gnats are said to sometimes spread damping off disease, but I don't know of any compelling evidence for this case. Favorable conditions for fungus gnats can be favorable for damping off, but that's as far as I say for sure.
I don't think fungus gnats attack plants. They eat fungus in the soil. They reportedly can bite and drink blood, though, but I've never seen or felt one in the act.