How can be any other parameters than the standard ones used in the current browsers and servers? I think they can't, am I right?

And how can browsers start to use any other parameters before they standardise them? I think they can't?

This is true but not particularly meaningful to me, because you can't really do anything new with crypto at all without some kind of software update. For instance, the primes and generator for conventional number theoretic DH are also pre-generated and baked into a standard.