Learn Polish: Nie da się kichnąć cicho. - It is impossible to sneeze quietly.

The -nąć suffix turns the imperfective verb kichać (to sneeze repeatedly or the general act of sneezing) into a semelfactive perfective verb. This means kichnąć refers to a single, instantaneous action—just one quick sneeze.

Since this is a general statement about what is impossible, shouldn't we use the imperfective kichać?

You generally use imperfective verbs for habitual or general statements. However, using the perfective kichnąć here emphasizes the impossibility of doing it even once. Saying nie da się kichać cicho would mean it is impossible to be a quiet sneezer in a broad sense, whereas nie da się kichnąć cicho zeroes in on the single act, meaning it is impossible to produce even one single quiet sneeze.

How exactly does nie da się translate to "it is impossible"?

The verb dać means to give, but the reflexive phrase dać się idiomatically means to be possible or to let oneself be done. Therefore, nie da się literally means it does not allow itself, which is the standard, everyday Polish way to say it is impossible to or it can't be done.

Could I use the phrase po cichu instead of cicho in this sentence?

Yes, they are very similar, but there is a slight nuance. Cicho refers directly to the physical volume of a sound (quietly, at a low volume). Po cichu can also imply doing something secretly, stealthily, or without drawing attention. Since a sneeze is a sudden physical sound, cicho is the most direct and natural fit here.