The use of Japanese is highly dependant on the context. In other words, whether or not the information is shared between speaker and listener is a key to select words. Identified information is usually omitted to reduce the redundancy.
- Would you like some tea?" be changed to "Sarah, want some tea?", or "Want some tea?" You would take out the 'you' and perhaps replace it with someone's name
Yes, you are right. あなた or second person pronouns are normally omitted or replaced to the person's name, because it can be identifiable for both speaker and listener.
By using second-person pronouns, you can indicate the distance of you and who you are talking to. If you feel close or try to be friendly/nice to the person, second-person pronouns are avoided or replaced to his/her name. On the contrary, if you would like to make a distant to the person, you can intendedly use the pronoun.
About あなた, some women use it to call their husbands or partners. In this case, it is not always used to make a distant but express the affectionate feeling.
君{きみ} is basically used to someone who you are superior to, i.e. your assistants if you are boss. However, it feels cold and a bit offensive.
The best to sound nice/friendly/polite in a conversation is not using second-person pronouns. If you feel awkward to do so, you can call the person's name.