1)
Why does David mention the good that he did for Achish? Achish himself said so, just he tells David to return to avoid envy!
1.
Malbim: David sensed the truth, that they suspect him, and he was inwardly happy. He wanted that also his men will not fight against Yisrael. Therefore, he suggested that he go with his men to fight [knowing that Achish would refuse].