This is almost 100% correct in terms of grammar and usage and is easy to understand. There are a number of places where it is "not idiomatic," not quite natural. These are mostly questions of writing style, not basic language. 

--This is correct, but "before" is slightly unclear. "a happy birthday" is perfectly correct and natural, but for some reason I would write it as a direct quotation. Thus, I would write this as:

--Last year I wished a German "Happy Birthday" a few days early, or

--Last year, I wished a German "Happy Birthday" before the actual date.

Furthermore we don’t have superstitions.

--I'd write:

--We have no superstitions in our family, or

--We are not superstitious in our family.

I wonder if wishing a happy birthday in other countries before time is bad luck too?

--I would rewrite this:

--I wonder if wishing people a happy birthday, in advance of the actual day, is considered bad luck in other countries, too?

--Are there other places where it is considered bad luck to give people their birthday congratulations early?

I can google it, but I appreciate a lot your personal comments.

--"Google" is the name of a corporation--a proper noun--and should be capitalized. That's true today. Perhaps in a few years, "google" with a small "g" will enter the language but until that happens, we should capitalize the g.

--For reasons I can't explain, "a lot" sounds better at the end of the sentence. And you should add the word "would" because it is hypothetical. It is easy to understand as you've written it, and in speaking it would never be noticed, but this is better.

--I can Google it, but I would appreciate your comments a lot.

Does this superstition exist in USA?

--You need to add "the" in front of "United States of America" or its abbreviation, USA. 

--Does this superstition exist in the USA?

Do you know it?