Hago consejos en español debajo así que no tengas que leerlo en inglés. Quizás me ayudes en aprender español y ojalá puedas entenderme. Siente la libertad de corrígeme si yo cometa errores.

Quieres decir ¨in adopting,¨ no ¨to adopt.¨ Los infinitivos de inglés no funcionan de la misma manera que los de español. Por ejemplo, para decir ¨El adoptar,¨ se dice ¨Adopting.¨

En ese contexto, deberías decir ¨like¨ o ¨such as.¨ ¨As¨ no es exactamente lo mismo como ¨como,¨ aunque son muy similares.

SO, YOU WANT TO ADOPT A PET? GREAT IDEA!

Esto es muy bien escrito. Me sorprendo de realizar que no hables inglés como natal, porque veía tan pocos errores al corregir. 

SO, YOU WANT TO ADOPT A PET? GREAT IDEA!

Dear Sir or Madam,

I send am sending you this email because I’m interested to adopt in adopting a dog. I’m a dynamic person who loves nature and I practice outside sports such as (or sports like) hiking and running. So a dog is the perfect pet for me and my hobbies.

Also, I have been living in a house for the last few years (or in recent years) with a big living room and kitchen and a pretty big garden which is awesome to install a kennel. My house are is in a suburb close to a river and forest.

Finally I would like to tell to you that I have had a dog for 12 years when I was a child and I know what kind of care a dog needs.

Yours Faithfully,
M.-

Woof! My corrections are in red and my suggestions to sound more natural are in blue/grey.

You could also use the conditional tense in a couple of your sentences:

"So a dog would be the perfect pet for me"

"a pretty big garden which would be awesome to install a kennel in"