You can use it, for example, when you and other people are talking about your preferences on something. Someone can start the topic saying: "Me gustan las películas de acción..." and when is your turn to speak, you can say: "A mí (it's like: "now, talking about me...") me gustan las películas de drama". In fact, this "A mí..." is quite natural when you want to express your opinion after listening other people opinion. So that "A mí..." is just something you use to enphasize that you are talking about you, to focus the people attention on you.

Hi! They both mean the same, the only difference is that the first sentence uses a "pronombre personal átono" (NOS) and the second sentence uses a "pronombre personal tónico" (NOSOTROS). You can use both indistinctly. http://www.livingspanish.com/Pronombres-atonos-tonicos-I.htm

I didn't understand the first part, I don't know if you wrote to complete a phrase :. "a me.......... me gusta......." , anyway, it could be a misunderstood from " a -mi- me gusta". About the difference between those sentences, there is no difference. I know in english you must to say always the noun, but in spanish the most of time you can avoid it, or actually replace it with another form which is more short.

Thank you, Monica!

You duplicate when you want to emphasize that you really like something or you love something.