The preposition "mit" requires Dativ, that's why it is "einem Kunden". The second part is a bit trickier. In English you use a preposition instead of dative case, e. g. "to write something to someone", in German "etwas an jemanden schreiben". That "something" is the direct object and usually expressed with accusative case in German. "to someone" is expressed with dative case in German, i. e. "dem Kunden". "Herrn Groß" is an apposition to "dem Kunden", It gets the same case as the noun it refers to. And yes, "Herr" is to be declined. Plural of "Herr" is "Herren", not "Herrn". So, you can distinguish it from the declination of "Herr".