Bad wheather 

Today in my city a bad wheather (weather).
I live in Ekaterinburg.
This city (both words mean essentially the same thing so use one or the other / city or place) in a  the center of Russia on an intersection of Europa and Asia.
Summer lasts some two months and begins come in autumn. 

(some means more than one so use one or the other / some or two - in this instance, "two" is used best in this sentence. Also, whenever a word number of more than one, e.g. two, three, four, five preceeds a word describing "how many," you want to pluralize that word by adding an "s" to the end. In this example we pluralize "months" in the example "two months.") 

(As far as the end of the last sentence "...begin come in autumn." This did not make sense to me, so to fix the sentence all I could see is that you meant "begins" in autumn. "Begins" means the same as "Start." And "come" means to move toward something. Please let me know if this is what you meant to write.)