I guess if you think it plays and feels great, then all its good! And it is a genuine Fender Japan (despite the random parts and aftermarket pickguard), so it was a fair trade.
I cant really tell only by the pics, but that is probably basswood, since most of the 90s MIJ Fender were basswood. Save for some models that had ash or alder bodys and USA made pickups.
Pickups look like standard Fender Japan with alnico magnets.
I briefly owned a MIJ 62 RI P-Bass a couple of years ago and it was a joy to play. It was white with black pickguard and rosewood board.
I think the only difference between the 57 and 62 RI was that the 57 had maple boards and 1 ply pickguards, as opposed to the 62 that had rosewood boards and 3 ply guards. I think the neck profile was the same on both models. Just like you said, wide and shalow, and the fingerboard was probably less than 9.5 inch radius. My favorite type of neck!