The head of the phrase controls agreement
A phrase can mention a plural group inside a singular expression. With keiner der beiden Termine, the head remains singular. Similarly, jeder describes individual members with singular grammar even when the statement covers a whole group.
Jeder Gast erhält eine Nachricht.
Every guest receives a message.
Two alternatives have several possible relationships
A choice between two options, permission to use either option and rejection of both options are different claims. State which relationship is intended rather than translating an isolated equivalent of either or neither without context.
Keiner der beiden Termine passt.
Neither of the two dates is suitable.
Negation can target the whole-group claim
If exactly three of five answers are correct, both all correct and none correct are false. Nicht alle preserves that limited claim without giving the count itself. Use a stronger negative expression only when the evidence supports excluding every member.
Nicht alle Antworten sind richtig.
Not all answers are correct.
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References
Original explanations and examples informed by grammar references. Level placement is an editorial teaching choice.