Learn Hardcore Swahili: Ni muhimu kugeuza mayai kwenye kikaango taratibu. - It is important to turn the eggs in the frying pan slowly.

It’s an impersonal evaluation: Ni muhimu = It is important, followed by an infinitive (here kugeuza) meaning to do X in a general way. You can say Ni muhimu kwamba..., but everyday Swahili more often uses either the infinitive (generic) or a subjunctive clause without kwamba: Ni muhimu ugeuze mayai... (It’s important that you flip the eggs).

Why is it kugeuza and not geuza or ugeuze?

kugeuza = infinitive “to flip/turn” (generic statement after Ni muhimu).
geuza = imperative “flip/turn!” (a direct instruction).
ugeuze = subjunctive “that you flip/turn” (after expressions like Ni muhimu, when you want to address a specific subject).

What’s the difference between geuza, geuka, and pindua?

geuza: transitive “turn/flip something” (fits here: flip eggs).
geuka: intransitive “turn/turn into/turn oneself” (the thing turns by itself).
pindua: “turn over/flip completely” (often stronger; e.g., pindua chapati to flip a flatbread).

Why is it mayai? What’s the singular?

Singular is yai (Class 5), plural mayai (Class 6). Agreement examples:

one egg: yai moja
many eggs: mayai mengi
fresh eggs: mayai mapya

Why isn’t there an object marker on the verb (like kuyageuza mayai)? Is that wrong?

With a stated, generic object, Swahili normally omits the object marker. Kuyageuza mayai is possible but implies definiteness/emphasis (“flip those eggs we’ve been talking about”). For a general instruction, kugeuza mayai is preferred.

What does kwenye mean here? Could I use katika, ndani ya, or the locative -ni?

kwenye kikaango = “in/on the frying pan” (very common and neutral).
katika kikaango = more formal; also fine.
ndani ya kikaango = “inside the pan” (literal “inside”; acceptable but less common here).
kikaangoni = using the locative suffix -ni, very natural: “in the frying pan.” Avoid juu ya kikaango (“on top of the pan”) unless you literally mean the outside top surface.

Is kikaango the right word? I’ve also seen kikaangio.

Both occur. kikaango is very common in modern usage for “frying pan.” kikaangio is also attested as an instrument noun. In some areas, people also say sufuria ya kukaangia (“a pot used for frying”).

Where should taratibu go? Can it come earlier, or do I need kwa taratibu?

Putting it at the end is very natural: ...kikaango taratibu. You can also say ...kugeuza mayai taratibu.... taratibu works on its own; kwa taratibu is possible but more formal-sounding. Sentence-initial Taratibu, ... is used in spoken language for emphasis (“Gently, ...”), but within the clause, end position is most common.

How is taratibu different from polepole?

taratibu = gently, carefully, in an orderly way (often implies care as well as slowness).
polepole = slowly (focuses on speed).
Both can fit in cooking; taratibu adds a “be careful/delicate” nuance that suits eggs.

How would I say “It’s important not to flip the eggs too quickly”?

Use the negative infinitive kuto-:
Ni muhimu kutogeuza mayai haraka sana (or ...haraka).
Here kutogeuza = “not to flip/turn.”