The difference between nǚ and nü is the tone mark. The first is third tone, while the second doesn't have a tone marked, ie it's neutral tone or whoever wrote it just isn't marking down the tones. As for nv, it's easier to type than nǚ, and requires no specialized knowledge of the keyboards special characters or anything. It's just turning into a character anyway, so why bother with the umlauts when a v is easier? You can write the ǚ properly when you actually need to show off the pinyin, but otherwise, it's not really worth it.

Hi Wenwei, as Seth has said, the difference between nǚ and nü is tone different. nǚ is nü with the third tone. It's not easy/convenient to type ü on any computer or cellphone. With my computer and cellphone, I have to install a special input method software which is for typing pinyin, and have to shift between the softwares, so that I can type Characters or English or Pinyin. So in some informal conversation, we use v instead of ü, which is easier.

the difference between nǚ and nü is the tone mark. nǚ is marked the third tone and nü is the neutral tongue. One thing you should pay attention is when ü comes with the initials j q x y, the dots should be removed. For example, yǔ, qū. About the 2nd question, there's no ü and also no method to type ü at the keyboard at first. So we choose v to take place of ü. Though we can type ü now, we get used to type v instead.