Jesus christ. ARCHONS AND ZEALOTS AGAINST LINGS AND ULTRAS. Have you even fucking thought that they wouldn't bring along DEFILERS for jesus christ's sake. And ultralings w/ defilers rape just zlots and archons.
What unit counters a hydra?
What unit counters a lurker?
What unit counters an ultralisk?
Finally, how do I expand and not let my expansion die?
Hydras are countered by almost anything- from dragoon to zealot. But if Z goes full hydras, that won't be enough as they'll be upgrading and massing faster than you can. You absolutely need HTs, and a shuttle full of reaver if you have em- and confident enough so you won't lose them either. But HTs are a must no matter what after a certain point of game.
If Z goes lurkers, I expect they'll go ling ultra def with some lurks. Upgrade, get reavers and don't get choked in- or you'll lose. Use some DTs to scout out some expos, and when you get through with lurks, you should have some sizable army- take out Z with it?
Lurkers can be countered by anything, but most effective is reavers and dragoons, or HTs with storms.
Ultralisks can be countered by dragoons, chons and dts, reavers, and storms.
And uh, not letting your expos die is a matter of having control over the center. You lose control of the center, or atleast parts of that lead to expos- then your expos are in danger- no matter what. And usually, late game requires tons of photons on expos too.
And note that everything changes when defilers come out. Dragoons become really ineffective against anything Zerg, and archons zealots and HT DT reavers become more powerful.
Also, you can't play PvZ with black and white logic where as some unit counters some unit because a P army is substantially stronger with more diversity.
None.