"He's just so annoying, I couldn't be more cheesed off with him." To be cheesed off is to be irritated or slightly angry. However it indicates only mild annoyance and would not be used to express serious anger.

Because to say somebody is mentally ill when they are not is considered rather rude. It implies they are abnormally, clinically unintelligent or that their behaviour is in some other way abnormal.

You've got two excellent answers in the comments section.

Yet and not just with the word proof. You don't need an article whenever a noun follows the verb "to be." So you say, "I am happy" not, "I am the happy." You say, "he is tall" not, "he is the tall." In exactly the same way you say, "this agreement is proof" because proof is a characteristic of the agreement.

"This book is written in Chinese and English" and, "this is a bilingual edition" are both fine.

You could add "the" if you wanted and the sentence would still sound find. When you use the word "after" it's not required, the article is implied. So you could say, "after accommodation costs it is around £20" or, "after the accommodation costs it is around £20" and both sound equally acceptable. "The Hopu and Bessert v. France case" is fine. You could also say, "the case of Hopu and Bessert v. France" or just, "in Hopu and Bessert v. France."

I'm not sure if there's a way to get every article. Here's one to get you started though: http://www.italki.com/article/444/transform-your-academic-english-skills-with-these-50-collocations#.VWbn_s_nuM8

Do you mean can you go from being an employee to being a student? If so the answer in the UK is no. The only way to become a student is to go through the standard admissions process. Working for the university might be something you could put on your application form when applying but you'd still need to go through central admissions like everyone else.