Did Mr. Earnshaw adopt Heathcliff because he had no children of his own?

No, Mr. Earnshaw has two children, Catherine and her older brother Hindley. 

Mr Earnshaw had two children, Cathy and Hindle but one day when he was out, he found Heathcliff on the streets of Liverpool and took him home.

this question has two way for answering: the first one as mentioned above. The second way for answering this question is when mr. Earnshaw brought heathclif to his own home, because of previously Mr. Eranshaw had a child named Heathcliff and he had been died for a certain situation, so he adopted Heathcliff for this reason

And that's so obvious from Hindely's heating for him