"who is truly like a son to me". Paul speaks of his close relationship to Timothy as though they were father and son. This shows Paul's sincere love and approval of Timothy. It is also likely that Timothy was converted to Christ by Paul, and so this is why Paul considers him like his own child
"God, who is our Father, and.". This refers to God the Father. It is best to translate "Father" with the same word that your language uses to refer to a human father.