Get a paper clip and push out the plugs in your USB connector. If your USB connector cable is too short then get and extension cable.

USB Color code

vcc / 5v = red
Ground = black
white = -data
green = +data

Keep the wires separate for USB1 and USB2.
Don't get you wires crossed between ports.

What color goes to what pin # ?
- I'm not that smart.

Pins No-pin and NC are not needed.

if pin #1 is the blocked pin. Then the row behind it is black then green then white and red at the end.

row #1 = Not needed / omit
row #2 ground - black
row #3 +data - green
row #4 -data - white
row #5 - red - vcc / 5v.

Look at example #2 and AC97.

Can I just Dremel the plugged hole away and then insert it ?

Yes, dremel the plug or just break it off that plugged up pin with a paper clip.

Hello
Tried to think on my own but it didn't turn out OK.
So what color goes to which pin on motherboard ?

No wait. Is it like this. Is this ok ?
What is the name of this 5-pin connector(female) ?

Those are Dupont plugs, you can find them in every possible size and shape you need for pc's. https://www.amazon.com/slp/dupont-connectors/8q78neyrmxzc6x5

Your last gif shows the right positioning for the mobo in your first post. My advice would be to use a double row 2x5-pin plug. If you plug in a single row pin the wrong way you may burn wires or worse.