Without going through each sample, it's hard to say what all you might have there. If it's not a commercial kit, it could quite possibly include a variety of files. However, most hardware samplers expect 44.1k/16-bit files - maybe said producer was just using his DAW.
On the sound you're hearing after converting(truncating) to 16-bit, yes, it's likely you can get some distortion from the process. The short answer to that is called Dither.
Good luck sorting the samples, you might have to go through them with an audio editor and see what's going on.