Amazon.com: buying info: Stats Player Profiles 2002 (Stats Player Profiles 2002)
I don’t think there is any evidence that players (in general at least) have a tendency to be better in the first half or the second half. But this book has all the available pertinent splits and situational stats on all players who had a reasonable amount of playing time.
It can get frustrating, however, because on players who didn’t see much time last year the splits are not complete. You can find much of the info you seek somewhere online, depending on what you’re looking for, at mlb.com, espn.com, sportsline.com, cnnsi.com or foxsports.com (they own STATS).
But the book has most of it in one place and is way more convenient. (Oh, and if you shop from that link up there I get a small cut.)