You capitalize Huntington
Yes, "Huntington Beach" should be capitalized because it is a proper noun referring to a specific city.
Yes, always.
No
If you are talking about it as a field of study you would capitalize it, but if you say I study math in general then not capitalized
If you are talking about the building in Washington, yes. If you are talking about a five-sided geometrical figure, no.
Capitalize your 'I'. I have no idea what you're talking about.
When you are talking about a specific university, you should capitalize it as a proper noun. When you are talking about universities as place, you can leave it lowercase. Which university does she go to? She goes to Stanford University.
If you are talking about father's in general, then no. You only capitalize it when you are talking about your specific father or the lord.
If you are talking about something with the title of gold, silver or iron like a book or a film then, yes, you would capitalize it but if you are only talking about the metal then, no, you wouldn't.
If you are talking about a particular person who has that exact title, then it is correct to capitalize Accounts Payable Administrator.
It depends. If you are talking about a specific highway like, Pan-American Highway, you capitalize it. If you are just talking about a random highway like, "Take that the highway till you reach Atlanta," then you leave it lowercase.
Talking about an unidentified chief I would not capitalize the word, but if I was using it as a title of a specific person, such as Chief Wiggum, I would capitalize it.