The word "nautilus" should be capitalized when it refers to the genus name in scientific contexts, as it is a proper noun. However, when used in a general sense to describe the marine creature, it should be written in lowercase. Always follow the specific style guide you are using for consistency.
The spelling is nautilus (a shelled octopus), or capitalized as a proper noun Nautilus (the name of a ship from Jules Verne's 20,000 Leagues Under the Sea, and the first nuclear submarine of the US Navy).
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.
yes
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 should not be capitalized.
The first 'c' should be capitalized.
Yes it should be capitalized.
Yes, it should be capitalized.
No. It should not be capitalized.