how do they come up with 10k 14k 18k in yellow gold ?

I presume you are referring to carats as a measure of gold purity. This is the fraction expressed in 24ths of the purity of gold. So 24 carat is pure gold, 18 carat is 75% pure and so on. The normal means of abbreviating carats is "ct" and most jewellery is either 9 or 18 carat gold as 2 carat is very soft.

The white gold isn't turning yellow - the issue is that your ring has been dipped to LOOK like white gold but is actually a yellow gold ring. The silver cleaner took the white gold dip off so the yellow gold is showing through. Go back to wherever the ring was purchased and just ask them to re-dip the ring. It'll look the same as before in no time!