Убедите собеседника в том что бы он не использовал полителеновые пакеты

Я бы перевела так (кое-где немного поменяла смысл, так что лучше перечитай):

"Dear Mary!

I want to invite you to visit me in Ekaterinburg . Besides you want to go to Russia, aren’t you ? I have holidays in the summer, could you come in June?  

Here is very good in the summer! I have already made a plan! I 'll show you Yekaterinburg, which is the capital of the Urals . We will visit the Museum of Stone Carving Art and the major temples and monasteries. You will see natural park " Deer Streams " .  

Another my  friend invited us to his dacha , which is located on the shore of picturesque lake "Baltic" . We will cook shashliks, swim and sunbath . Also I’ll introduce you to my friends. We will have fun !  

If you agree , then write more . I'll tell you how all things should be done. We will take all your expenses in Russia . Besides you will live with my sister , we have have prepared for you a separate room.

You friend, Lena."