Yes it should be capitalized.
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.
It should only be capitalized if it forms part of a title.
Yes it should always be capitalized.
Yes it should be capitalized.
As an abbreviation it should be capitalized.
No. It is a proper noun which means that it should always be capitalized. You should always right it as Buckingham Palace.
Yes, if "Fun" is part of the official title of something, it should be capitalized. If it is just a descriptor in the title, it would depend on the specific style guide or preference of the author.
No. It's not necessary
Not necessarily.
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.
"Japanese" is capitalized incorrectly. It should be lowercase in this context, unless it is part of the proper noun for a specific group or organization.
It should only be capitalized if it forms part of a title.
As an abbreviation it should be capitalized.
Yes it should be capitalized.
Yes it should always be capitalized.
No it should not be capitalized.
The first 'c' should be capitalized.