Learn Polish: Jestem ciekaw, czy jutro będzie sztorm. - I am curious if there will be a storm tomorrow.

ciekaw is a short-form adjective. A few Polish adjectives have this special short version which is used only when the adjective comes directly after the verb 'to be' (as the predicate). If you were attaching the adjective directly to a noun, like 'a curious boy', you would have to use the normal full form ciekawy.

Can a woman say this exact sentence?

No, a female speaker cannot say Jestem ciekaw. The short form ciekaw is exclusively masculine. A woman would use the standard feminine adjective and say Jestem ciekawa.

Why does this sentence use czy for 'if'? Shouldn't it be jeśli?

In English, the word 'if' has two meanings, but Polish splits them up. When 'if' means 'whether' and introduces an indirect question or uncertainty (like wondering if it will storm), you must use czy. You only use jeśli for conditions, such as 'If it storms tomorrow, I will stay home'.

I learned that 'storm' is burza. What is the difference between burza and sztorm?

burza is a standard inland thunderstorm, usually with rain, thunder, and lightning. sztorm specifically refers to a storm at sea or a very severe coastal gale. The speaker here is likely near the ocean or planning a boat trip.