1. It depends why he's testing free agency. If, for example, he dislikes you because you beat him in arb 3 times, he won't change his mind. However, if he's testing the market because he thinks he can get better money for his skills, he may change his mind if his overall rating decreases between this season and next.
2. Again, it depends on his rationale for leaving, but you can pretty much take #1 and reverse the answers. If he hates your team, he may sign with the team he gets dealt to. If he wants to just go get a better contract for his talents, the new team may be out of luck (but could always get lucky and have him change his mind).