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).
yes
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.
Yes, "Osprey" should be capitalized because it is the proper name of a specific bird species.
Yes, "Local Park" should be capitalized because it is a proper noun.
It should only be capitalized if it forms part of a title.
Yes, it should be capitalized.
The first 'c' should be capitalized.
Yes it should be capitalized.
Yes it should always be capitalized.
As an abbreviation it should be capitalized.
Yes it should be capitalized.