True or False answers
On the Kaz Matsui question, "Kaz Matsui will improve this year, raising his batting average to at least .285, with OBP of at least .345 and SLG at least .420," my answer for that is False. I do think he'll improve in the power department, but given the park and league context, I don't see his batting average getting much higher than it was last year. But I do think we'll see more power out of him.
On the Andruw Jones question, "Andruw Jones will have his best season after the age of 30," I think the answer is True. Although his skills seem to have stalled right now, he's only 28 and I think he will age well. In the comments, people mentioned that "best season" is pretty vague, and even if he has a stunning offensive season after age 30, the decline in his defensive skills may make such a season less valuable in the aggregate as measured by "player totality" measures like VORP or Win Shares.
When I asked the question, I was thinking of offense and wasn't considering defense. So my "True" answer is just in relation to his bat.
Most Similar Players to Andruw Jones, through age 27
Ken Griffey JR
An intriguing mixture of the Great (Aaron, Bonds, Robinson, Griffey, Mathews), the Near-Great (Santo, Kaline), and the Very-Good-but-Somewhat-Disappointing (Sierra, Canseco, Luzinski).