No it shouldn't be capitalized.
No, "hospital system" in general is not capitalized. However, if you are referring to a specific hospital system by name (e.g., "Mayo Clinic Health System"), you would capitalize it.
Yes, "World's" should be capitalized in the phrase "The World's first hospital" as it is a proper noun referring to a specific hospital.
Yes, the word "Hospital" is capitalized when referring to a specific, named hospital. For example, "I work at St. John's Hospital."
It is not necessary to capitalize "system software" unless it starts a sentence or is part of a title.
Yes, "Salt Lake County Criminal Justice System" should be capitalized as it is a proper noun referring to a specific entity or organization within Salt Lake County.
Yes, you should capitalize "Federal Law" as it refers to the specific legal system or statutes established at the national level by the government.
Yes, "World's" should be capitalized in the phrase "The World's first hospital" as it is a proper noun referring to a specific hospital.
no
No
Yes, "Salt Lake County Criminal Justice System" should be capitalized as it is a proper noun referring to a specific entity or organization within Salt Lake County.
No. It's not necessary.
Yes, the word "Hospital" is capitalized when referring to a specific, named hospital. For example, "I work at St. John's Hospital."
It should be capitalized if you are referring to a specific metro system.
Yes, you should capitalize the C in Century.
You should capitalize it if it is a brand name.
No, you should not. You should only capitalize a word when it is at the start of a sentence or when it is a proper noun.
No
no