Is it true that because of the vowel harmony some sentences or words always have the same vowel in the word following? I mean, after 'var' do you always get 'mı'? And after 'değil' is there always 'mi'? After 'yok' always 'mu'? Does it really not matter what you say before 'var', 'değil' or 'yok'?

e.g.
güzel mi? / güzel değíl mi?
şíşman mı? / şíşman değil mi?
memur mu? / memur değil mi?

Yep, as far as I know that's true!

The main idea of vowel harmoney,is o make pronounciation more easier on your tongue.
So when you pronounce a thik vowel in a word,you follow it with same harmony as a thik vowel too.
And when you pronounce a thin vowel in a word,you would follow it with same.

İt has been explained marvelously by aslan2 before.

İf you want,try to look his old posts up,you will find it in his profile,and search it.
İt will be great help to you.