the chain, yes, that could easily be changed to a different type/length/metal/etc.
as for the diamonds, yes, that could also be done however expect that to cost substantially more than you would expect. Because chances are the majority of those teensy-tiny prongs would need to be retipped, and then have seats cut to hold the new stones. plus the charge to remove each of the stones currently in there.
that's a really pretty necklace!