Nothing to wonder there!
This is my friend
That is yours, and
Here is hers.
Likewise...
Friend of mine
Friend of yours, and
Friend of hers
Hers -pronoun's possession.
Do you know a friend of hers ~ Yes, I know a friend of hers (fit in the above example).
The sentence reads a friend of... and is singular. Hers there is as defined above.
Good points to note are CopperKettle's and Oerkelens'.
The word your already denotes the possessive. In English, possessive adjectives do not need 's at the end, the adjective does that job along with identifying the owner.
I am my own friend.
I am your friend.
I am his/her/its friend.
I am our friend. (Doesn't make much sense, but it's grammatical and shows the pattern.)
I am your friend.
To keep things confusing for our English Language Learner friends, English does use a plain s (usually) at the end of the possessive pronouns to change them from being adjectives to nouns.
Whose friend are you?
I am mine.
I am yours.
I am his/hers/its.
I am ours. (And again, nonsensical, but grammatical.)
I am yours.
In short, your's or his's is never grammatical, nor would yours's or hers's be.
Regarding your second question, the common English pronouns are:
- Person: Subject, Object, Possessive Adjective (aka Personal Pronoun or Personal Determiner), Possessive Pronoun
- 1st person singular: I, me, my, mine
- 2nd person singular: you, you, your, yours
- 3rd person singular: he/she/it, him/her/it, his/her/its, his/hers/its
- 1st person plural: we, us, our, ours
- 2nd person plural: you, you, your, yours
- 3rd person plural: they, them, their, theirs
Note: This is in no way intended to be a full list of English pronouns; there are a fair many more. (Ex: This, that, these, someone, etc) However, the others are either treated as normal nouns when making possessive forms or they don't have sensible possessive forms at all. These are the ones that seem to be causing you confusion.
Without researching the words' etymologies, that's pretty much all I can tell you. English doesn't distinguish between singular and plural in the second person at all, and those are the pronouns we use. The Wikipedia article for this explains some of the history, but it doesn't include any real rationale for why the current forms are what they are.
Best Answer
I think you're largely on the right track.
However, I would assume that “A friend…” was indeed a friend of yours – not a friend of a friend. However, the use of a (instead of the more familiar and intimate my) might suggest the person is more of an acquaintance than a close friend, but that's not necessarily a given.
I don't think “One of my friends…” is too wordy. It might be especially useful if you remember hearing something from someone, but you can't quite remember which friend gave you the information.
Also, instead of “told me”, I might be more inclined to simply use “said”.
Lastly, I think there's one viable option you've left of your list: