If you're going to compare to a natural language, you need to use the language correctly. Saying "If paused then..." is not correct English, as it lacks a subject. Used correctly you would say "If the recording is paused..." So the more verbose comparison (if(a == true)) is actually the form used in English.
I don't follow this. The translation of "if(paused == true)" to english would be something like "If it is true that the recording is paused".
When I use a variable of type bool.People warned me:you'd better written if(a == true) as if(a). I do not know why we must do this.
I'd advise the opposite, don't compare with the literal value for boolean variables.
What are the advantages of doing?
It is mainly stylistic, though as others have mentioned there is actually a subtle difference between the two, as a boolean variable can actually have values other than true or false.