A friend has sent me an email with questions scattered throughout ending in 〜のですか, should I have 〜のです at the end of all sentences that address/answer those questions in my reply? (EDIT: Because I've seen examples in textbooks between two people where A asks B something using 〜のですか and B answers with のです)
Without knowing the actual questions asked and your (intended) answers/replies to them, it is difficult to answer this question with authority, but generally speaking, the following could be said.
Basically, you do not need to use 「のです/んです」 in your answers/replies to questions ending in 「のですか/んですか」 except when you want to emphasize a statement as in saying something along the lines of: "X really is this way in my country". You would need to be quite certain that the information you are giving would be "news" to the other person.
It is completely acceptable to use 「のです/んです」 in some of your "answers", but it would sound pretty wordy if you used it in too many of them. That is because 「の（or ん）」 is such a nuanced word despite its physical length and simple appearance.
I would say that if you used 「の/ん」 in roughly over 1/4 or 1/3 of your answers/replies, you would be using it too many times. Then again, I am saying this without knowing the content of the emails in question, so please take it with a grain of salt.
I think the best way to answer those questions is to answer those in polite forms.
Japanese tend to add の at the end of sentence to make it more natural. Japanese people if I'm not mistaken are always delighted if you address them in polite form.
The example above is the plain form of the question どこに行きますか。
To me ‘の’ of …のですか？and ’の’ of ’ …のです’ looks somewhat superfluous, though I’m not saying it’s wrong. If the question is asking whether it’s your possession, you can say これはあなたの(物)ですか？はい、私の(物)です。
The typical form of question in the polite way ends with ‘ですか？’and affirmative answer is 'です’ or ‘ます.’ That’s why we call 敬語-polite way of saying ‘です・ます調- desu/masu style’
There are many ways of ending the line in asking and answering question. So I cannot generalize how to express it. What I’m saying is you don’t need to stick to insertion of ’の’..
The use of の at the end of a sentence is used only when seeking or providing an explanation or extra information on a particular subject.
例： 「何それはのですか？」(What is it?)
「ししおどしと言いますの。」(It is called 'shishiodoshi')
NOTE: ししおどし refers to those really cool bamboo fountain spouts, by the way. There isn't any one word to capture the meaning in English though.