As Tom has explained, someone else’s age is not usually considered any of your business in English speaking culture. It may or may not be rude, but it’s weird, and people may think you discriminate based on age / youth (or perhaps you’re looking for personal data you can use to impersonate them). As far as women, note that these days, we use “Ms” for all women regardless of age / marital status, so there’s no reason to determine either in order to choose the right form of address. If you ask someone their age, they’re certainly going to wonder *why* you’re interested….

It all depends on context. There are some circumstances in which it would be essential to know the age if you didn’t want to get arrested!

Definitely

It is probably rude to ask anyone their age unless you are talking to a child under the age of 10 or you are a government official at the passport office and you have a good reason to know someone's age. Once people reach 35-40 most would tend to prefer to be thought of as younger than they really are - this is especially true of women, it seems to me. But different cultures have different ways of looking at this, I'm sure.