a try to wrire write an informal letter

Moscow,
Russia,
12 nNovember 2017

Dear Bob,

Thank you for your last latter. How are you? How is your family? I hope you are well.

Comment :  It is also correct to say "How are you and your family" and combine two questions on related items.

I was so surprised to hear that you have pets: two cats and a dog. How What are their they names?
I like animals  not only pets. They are so different and a lot of animals help people.

Comment: You can say "I like all animals" or "I like animals, but not only pets".

Comment: If you wish to say много видов you can say  "There are many kinds and a lot of them help people." or "There are many types of animals and many of them help people." 

When I will am grown up I want to be a vet. I want to take care of about animals.

By the way, my grandmother give gave me two parrots on Suaturday, on my birthday. I will send you their photo.

Comment: Give =дайте.Gave = дал.

Comment: If you are sending both in one photo than your language is correct.  If you will send a picture of each parrot then you will be sending two photos.

Maybe you could [see comment]  to visit me on holiday? We can go to ski together or to skate. I look forward to your reply.

Comment: You could say "could come to visit me" or "visit me on...".
Best wishes,
Kathy

a try to wrire An attempt (try) at writing an informal letter

Moscow, Russia
12 November 2017 << always capitalize the months :)

Dear Bob,

Thank you for your last letter. How are you? How is your family? I hope you are well.

I was so surprised to hear that you have pets: two cats and a dog. What are their names?
I like all animals, not only those we keep as pets. << (that is a suggestion that emphasizes your love for all animals)  They are so different, (for more clarity, you could say: 'there are so many different kinds') and a lot of animals help people.  When I grow up I want to be a vet. I want to care for animals. << (care for means 'to take care of'). 
By the way, my grandmother give me two parrots on Suturday, which was my birthday. I will/ can send you their photo. 

Maybe you could to visit me on holiday? We can go to skiing or skating together. I look forward to your reply.

Best wishes,

Kathy

a try An attempt to write an informal letter

Moscow,
Russia,
12 November 2017 (If you are writing to an American, Americans like to write the date backwards so it would be November 12 2017)

Dear Bob,
Thank you for your last latter. How are you? How is your family? I hope you are well.

I was so surprised to hear that you have pets: two cats and a dog. What are their names?
I like animals, and not only pets. They are all so different and a lot of animals help people. When I will a grown grow up I want to be a vet. I want to care about take care of animals.
By the way, my grandmother gave me two parrots on Saturday, which was on my birthday. I will send you a photo.

Maybe you could to visit me on holiday? We can go to ski together or to skate. I look forward to your reply.

Best wishes,
Kathy