In the house of Simon (εν οικια Σιμωνος). See 9:43 for παρα Σιμων with same idea.

Cornelius told all about his vision, described how he sent for Peter, and invited him to relate “everything the Lord has commanded you to tell us.”…

Send therefore to Joppa (See Gill on Acts 10:5), (See Gill on Acts 10:6).

who when he comes will speak to you<…

When we see our call to any service as clear, we should not be perplexed by doubts and scruples arising from prejudices or former ideas.