In my History book, wherever there is written about the monarch of Russia 'Tsar Nicholas II', they write 'the Tsar'. Why is 'the' used before a person's name? And even if it is, then why isn't the 'T' capital?
"Tsar" isn't his name. It's a title and it's also the name of his role or position. Just as we would write "the King", "the Emperor", "the Prince", "the Pope", so too we write "the Tsar". The "the" is mandatory is here.
By contrast, if we are using "Tsar" (etc) as a title, there is no article ("Tsar Nicholas II", "Queen Elizabeth "II", "Pope Francis").
Similarly, we refer to "President Trump" but to "the President".
In "Tsar Nicholas", the capitalisation of "Tsar" is mandatory. In "the tsar", it is a matter of style, and preferences or house styles may vary (some favour lower case - http://www.chicagomanualofstyle.org/qanda/data/faq/topics/Capitalization.html ), but it is often capitalised, especially if it refers to a particular individual (see http://www.uwyo.edu/english/eighteenth-century-life/style_guide-4.html ).