I went through google search to find your email address, and eventually I succeeded in finding your email address.
Is this sentence correct?
your sentence is ok but avoid repetition . Use instead of "your mail address"
"it" and capital letter for both Google and Search
I didn't like "and eventually" .Plz drop the "and" and use ";"
I went through Google Search to find your email address; eventually I succeeded in finding it.
You could also say, I googled for your email address ...