Only in the plural. You can have a brother in Christ, or several brothers or brethren in Christ.
"Brethren" almost invariably means religious brothers of some kind.
"Brother(s)" can mean:
metaphorical brother(s) (in Christ, in arms, in a college fraternity, etc.)
fellow black/African-American men or boys (if you're not black, you probably should not use "brother" in this way)
Yes, apart from plural 'your', ваш is also a more polite version of singular 'your' (твой) . Just as вы is a more polite version of ты. You use it with elder people, strangers, people in authority and people in other formal occasions. When in doubt what to use, always use вы/ ваш, except in clearly informal occasions to equals or younger people.
The genitive only appears in those phrases because objects of the preposition "у" take the genitive case. I think you're asking why ваш isn't genitive? Well just like English, possessive pronouns sort of get to be a separate class of words, that's why pronouns in English don't become possessive by adding 's.
The genitive in Russian occurs in the same situations it would in English (you can think of English genitive words as being words with 's or words that follow "of), plus in cases where the words before forces the genitive case.
There are, although they're far less prominent than in Polish. https://en.wikipedia.org/wiki/Vocative_case#Russian
Okay, thanks. So long as I wasn't missing something else which should be different. I will look out for ?s in future! By the way, you seem to be a human, rather than a bot, so I would like to add a general comment on my impression of this Duolingo course. It is very good and relatively effortless, but perhaps it could add some suggested daily vocabulary lists (of the most common words), because that is something which takes time to build up, and is just as important as grammar.
Thanks for your assessment of me being a human. But I am just another 'student' like you. But if you want to practice vocabulary, I can recommend de 'Tinycards' app, also from the makers of Duolingo. It has all sorts of training material. Among that also the original vocabulary of this Russian course by Duolingo. I use it myself and it is very useful.