1) Short answer - because grammar. Long answer - in Russian, unlike English, words change according to their specific roles in a sentence, the whole issue is too complex for me to just write it all down for you and you'd have to go through some grammar books or countless hours of experience to figure it out on your own. English also has this or a remnant of this with pronouns such as she, he, they turn into her, him, them respectively. As for this particular example you can read up on "genetive case" in Russian.

2) No, it's not grammatically correct. Again, because you don't seem to have the faintest idea of actual Russian grammar. I didn't say that to offend or patronize you or whatnot. I'm sure you'll quickly learn all about that if you put your mind to it. So good luck and yes, what "you saw somewhere" is how you say it properly.

3) Yes and no. Моя друг is not possible, because we have a specific feminine version of this word, which is подруга. You have to use that with моя - моя подруга. It's actually hard to think of an example where actual gender wins out and папа is not a proper example of that as it is obviously a word that exclusively describes a male person and therefore the word is of masculine gender by difinition, even if it looks like a femenine form with that -а at the end. This precedence can only take place if a word that's grammatically masculine can be used to describe both males and females and there is no proper femenine version of that word. Job descriptions is where you should look here as they kind of default to masculine gender but women can also occupy those positions now if not back when the job was invented. In fact I think I might have come up with something suitable here. Директор is masculine but both men and women can be that and there's hardly a good feminine variant of that word, well there's директорша but it's very colloquial and some, if not most, women can even find it offensive. In any case you can say something like:

Хорошая директор у вас - You have a good (female) principle

That would be acceptable although many would still prefer to stick with masculine there, even if they talk about a woman.