"Mencionó" because "mencionaba" would need to specify the times when he used to avoid mentioning the existence of his cat. "Mencionó" underlines "nunca" in the sence of "not once".
"Tenía un gato..." because the speaker talks from the point of view during which the cat used to live there. If they said "tuvo un gato..." might have suggested a short period of time.
__________________
♪ ♫ ♪ Ain't it wonderful to be alive when the Rock'n'Roll plays... ♪ ♫ ♪
|