Usage of articals. e.g. When do we use a singular noun on its own without an article?

Solution 1:

The explanation given in the Oxford Guide to English Grammar ("We use a singular noun on its own only in some special patterns") is not particularly useful. More helpful is the following extract from Collins Cobuild English Guides 3: Articles (p50) in the section called Special Roles:

Some nouns can refer to a special, unique role held by a person in a particular situation (for example, a government or business). When they are used like this, you can leave out the definite article.

• ...when he was President.
• It was nearly 40 years before she became Queen.
• ...Mr John Hume, leader of the Social and Democratic Labour Party.

The Guide goes on to list numerous examples of 'special roles' (including captain, chair, boss, treasurer, director, author), and concludes:

Note that when you are talking about a person rather than describing someone's role you need an article.

• The President had issued a sympathetic reply.
• The Queen then abandoned the project.

Since you have not included the sentence in which you saw the words Leader of..., it is not possible to say definitively if the definite article is needed or not.

Finally, a comment: Your Q2 is best asked as a separate question.