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Words like apex, peak, pinnacle or acme are usually used to describe the most successful, powerful or exciting part of something.
Is it okay if I use them for the maximum point of a bad situation? If not, what word can I use then? (any word other than maximum)
For example:
In 1870s, the sense of frustration reached its ............. .
You might call this point a crisis.
From the Cambridge Dictionary:
crisis
[...]
an extremely difficult or dangerous point in a situation:
crisis talks
A mediator has been called in to resolve the crisis.
US also crisis point a moment during a serious illness when there is the possibility of suddenly getting either better or worse:
He's passed the crisis - the fever's started to go down.
I would take care, however, to make it clear from context that the intention is not to invoke the first definition in that dictionary, which is "a time of great disagreement, confusion, or suffering."
Peak sounds best to me, and pinnacle or apex would work as well I believe (maybe acme would too but I just never see it used).
You could also use peak as a verb there - "the sense of frustration peaked" (but not piqued or peeked! -.-).
As antonym to the examples you give (and as direct antonym to zenith), consider also nadir. From the Oxford Living Dictionaries:
nadir
NOUN
1-The lowest or most unsuccessful point in a situation.
2-(Astronomy) The point on the celestial sphere directly below an observer.
A word often associated with difficult situations is crux.
The decisive or most important point at issue.
A particular point of difficulty.
Also, at dictionary.com
a vital, basic, decisive, or pivotal point
Example from Mandates Reasons, Results, Remedies
It must not be forgotten that agitation reached its crux during the depression.
Example from BBC News
The number of men entering seminaries reached its crux in the 1960s, Father Embery says, leaving a top-heavy age profile within the priest population.
