I have found posts that say having Zeta already will be beneficial is some way or another. That is not my worry. What I'm concerned about is, if I'm now at Nexus stage, will I be able to continue the relic questline to the (current) end in the expansion? Or will it disappear from the game.
You will be able to.
Does that also go for other classes? That I can do each and every phase of the relic chain to all classes with whcih I haven't even started it yet?
I'm pretty sure the only things they're going to do with the current relic questline, is making it easier, and making it so that you can get statless copies of any previous stage of your relics for glamour.
Yes, the relic quest is going to stay in place. The new jobs will not have relics associated with it, however. Yoshida mentioned making the 2.0 relic chain easier to complete, so if you're interested in collecting them for (glamour or just for shinies), you'll be able to.