If you are informally referring to someone in your family, it is not necessary except for emphasis.
If it is the proper name, say for a character on TV or in a book, yes then you'd capitalize it.
At our family picnic, big John found little John down at the lake.
Big John and Little John enjoyed entertaining people with their clown act.
Yes. It should be--- Little League Team.
Yes, since it is a pronoun.
No. You only need to capitalize the word "trust" or "trustees" when you are referring to the specific trust. For example: As referenced in the John Doe Revocable Living Trust. John Doe, as Trustee for the John Doe Revocable Living Trust. However, if you are simply refering to the trust, you do not need to capitalize the word trust. The above-mentioned trust contains limited authority for the trustees.
Do not capitalize little words within titles such as a, an, the, but, as, if, and, or, nor, or prepositions, regardless of their length.
big fish, little pondto be a big fish in a little pond
Big John Little John - 1976 Big Scare Little Scare 1-5 was released on: USA: 9 October 1976
Big John Little John - 1976 Big Shot Little Shot 1-6 was released on: USA: 16 October 1976
Big John Little John - 1976 was released on: USA: 11 September 1976
Little Laura and Big John - 1973 was released on: USA: May 1973
Little Laura and Big John - 1973 is rated/received certificates of: USA:R
Big John Little John - 1976 The Missing John 1-11 was released on: USA: 20 November 1976
Big John Little John - 1976 Abracadabra 1-13 was released on: USA: 4 December 1976
Big John Little John - 1976 Peter Panic 1-2 was released on: USA: 18 September 1976
Big John Little John - 1976 A Sizeable Problem 1-1 was released on: USA: 11 September 1976
Big John Little John - 1976 The Great Escape 1-4 was released on: USA: 2 October 1976
John Tower went by The Little Big Man.
Little John is one of Robin Hood's associates in Sherwood Forest.