most people want it because it is rare
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No a PSP
No only portable is Nintendo DS
No, there is not any Pokemon games for PSP because Pokemon is made for Nintendo. The PSP is made for Sony. So if you want to play Pokemon you would have to buy a gameboy or a DS.
Yes. The Nintendo DS has the same headphone port as the PSP, so the headsets can be used on both. It is probably recommended, though, that you use the PSP headsets for the PSP only, considering that it was designed for the PSP. In practice, you may use them for both. Source: I own a PSP and a DS :)
Diamond and Pearl are Nintendo DS games, and are not digitally distributed.