Could dark matter particles be unstable? Is it possible that dark matter particles are unstable and the existing dark matter will decay in the long run and turn into hydrogen, for example? What would be possible mechanisms for such a decay?

Could some of the hydrogen we observe be "new" hydrogen, i.e. be the product of dark matter decay?
Yes, as mentioned elsewhere, it is possibly possible. Dark matter particles may be intrinsically unstable (though having long lifetimes, which are at least significantly longer than Hubble time).

Check for more info here:
http://arxiv.org/abs/1307.6434