Juan Sierra and my partner Beer

Chaikaew,

Thanks for writing about your partner, Valeria. You come from two hometowns that are very far from each other, but both have some similarities, for example climate.

I have written a new version of your introduction. When you have time (why not now?), you should look at it and learn from the changes.

(new version)

Hi, my name is Chaikaew Nuttharin, and my partner's name is Valeria.

The name of my hometown is Thailand, and my partner's hometown is Mexico.

(note: Thailand and Mexico are countries. A hometown is a city or state or village.  For example, I am from the United States, but my hometown is New York. 

She told me that the population in her hometown is Mariachi. It's a form of folk music from there. The population in my hometown is about to Buddhist temples.

(note: "population" means the number of people. For example, the population of New York City is about 8,000,000. I think the right words for your sentences are "popular thing":

She told me that a popular thing in her hometown is Mariachi. It's a form of folk music from there.  Popular things (plural) in my hometown are Buddhist temples (plural, more than one). 

(original  version)

Hi, my name is Chaikaew Nuttharin. and my partner's name is Valeria.

The name of my hometown is Thailand, and my partner's hometown is Mexico.

She told me that the population in her hometown is Mariachi. It's a form of folk music from there. The population in my hometown is about to Buddhist temples.