20mAh is a (very, very small) battery capacity and nothing to do with LEDs. I think you mean 20mA.
The LEDs do not need 5V. They need something between 3.0V and 5.0V, and each led can be different. If the led you connect needs 3.0V and you connect it to 4.2V with nothing to limit the current, it will be damaged. In practice, most will be closer to 3.5V.
Because the amount of light from each color will have different intensity. If you want identical intensity, then the current will be different for each color.
I don't know, it is strange. I would expect red, orange and yellow to have a lower typical voltage than blue and white. I wonder if that data sheet contains errors.
These are more like the forward voltages I would expect:
Ah, yes, I completely missed that on the data sheet you linked to. It says:
5mm Round Flashing LED
2.4Hz 1/12 Duty Cycle
So maybe the voltage requirement is that if the built-in flashing circuit/chip. Since the voltage range is the same for all led colours, that may mean that the circuit includes a constant current source. If so, no external current limiting is required.
Now I think I can answer your original question: you cannot connect these LEDs in series, their built-in driver circuits would interfere with each other and would not work. You must connect all your LEDs in parallel across the battery.
Again, you cannot connect these LEDs in series, they must be connected in parallel. If you connect two batteries in series, the voltage would be too high and damage the LEDs (their Max voltage is 5V).
Connecting 2 batteries in series does not increase their capacity, only their combined voltage. Connecting 2 batteries in parallel increases the capacity.
Thank you @PaulRB , so if I connect these LEDs in parallel to 1 battery without a resistor, how many can I use? (I need the light to work for about 10 min.) before I recharge the battery.