1. They are much alike in character.
2. They are much alike in personality.
(Are both the same? Which word is commonly used?)
3. There is a letter for you from your mother.
(Does 'for you' modify'letter'? Does 'from your mother' modify 'letter' as well?)
I'd use 1 more often than 2.
In 3, both prep phrases are modifying "letter" yes.
1. Both sentences convey the same meaning. The phrases "alike in character" and "alike in personality" are used interchangeably to describe similarities in someone's character traits or qualities. The choice between using "character" or "personality" depends on personal preference or context.
2. Yes, both phrases, "for you" and "from your mother," modify the noun "letter."
The phrase "for you" indicates that the letter is intended specifically for you. It suggests that the content of the letter is addressed to you or pertains to your involvement in some way.
The phrase "from your mother" tells you who the sender of the letter is. It indicates that your mother is the one who wrote and sent the letter.
Both phrases provide additional information about the letter, specifying its purpose and origin.