Hello. Which case of the pronoun do you use in possession? Is it genitive? According to this website http://www.russianlessons.net/grammar/nouns_genitive.php they use the 3rd person pronouns without the "n" letter in front.
The examples you provide above are what we call in English "possessive pronouns" (for 3rd Person point of view). Does Russian have any sort of equivalent to the English "possessive adjective" (also called the "possessive determiner")? The differences are slight (in English), so I've added a chart below to show you what I mean:
To use this prompt as an example:
The chart below breaks down the part of speech for gender, person, and case. It appears that Russian does not distinguish between your/yours, her/hers, their/theirs, and our/ours. In other words, you use the same word for both, correct?
I realize that we don't hit lessons on possessives until a few tree branches down the road, but I thought it might help some to see the difference between these constructs now.
Yes, in Russian there is no difference between "your" and "yours" but we have different forms of твой for 6 cases, 3 genders, plural. Removing duplicates here is full sorted list: твоё, твоём, твоего, твоей, твоему, твоею, твои, твоим, твоими, твоих, твой, твою, твоя. Same for other pronouns.
isnt кошка the diminutive of кот?
It's not. It's the actual name of the species (and also a female cat). "Кот" is specifically a male cat. The diminutive of "кот" would be "котик". The diminutive of "кошка" would be "Кошечка". (though one con form other diminutives using different suffixes, these are simply the most obvious and simple ones)
Yes, but only in formal styles and it depend on author's decision. See comments in this course: CONTRARY TO WHAT MANY NATIVE SPEAKERS HAVE COME TO BELIEVE IN THE LAST TEN OR FIFTEEN YEARS, THE POLITE "YOU" IS NOT AUTOMATICALLY CAPITALIZED IN RUSSIAN, AND NEVER WAS. SUCH CAPITALIZATION IS USED IN SOME FORMAL STYLES.
It's how I was taught at school. And I am Russian. And I was not the worst student :) Of course I was going to school many years ago and I am not an expert, but it's my native language. And all people who I know still using capital letter for polite form. It looks " more properly" - something like this. But "no one die" if you will not use this rule :) , it's up to you.