Yes.
Yes.
You do not capitalize "president'. You only capitalize "president" if you are using it with a president's name. EX: The president is tall. EX: The tallest president was President Abraham Lincoln.
Yes, you should capitalize 'President' when it refers to a specific person ('The President of the United States'). It should be left uncapitalized when it is non-specific (Past presidents have included ... ').
yes you do
Yes.
no
If you are addressing someone as the president then yes you do capitalize it.
Yes it should be capitalized.
Yes, President is a title just like professor. Its acceptable to not capitalize these words when they are not describing someone. EX: the history professor is really difficult. But when it is not a noun, and is however, a pronoun you should capitalize it. With the exception of President and Doctor. These should for the most part always capitalized.
No you don't.
no
Yes, usually it's proper to capitalize President. When simply saying 'the President,' it's proper to capitalize it but okay not to. However, when you're saying 'President Obama' as his title, it's required.