"Ja mam czapkę."

Translation: I have a cap.

[RicardovanBelzen]

Is this a female word with czapka as nominative or is it neuter, with chapkę as nomanitve? Or is it neither and is it something in the nominative?

[Jellei]

A feminine word "czapka" put into Accusative (declension here).

"to have" takes Accusative in Polish. When negated, it turns into Genitive.

[RicardovanBelzen]

Thank you, I understand it now. But it's a very difficult language, Polish..

[Austin.Boston]

Why do you say je mam when mam means I have?

[Jellei]

"JA mam".

Because you can. The fact that "Ja" is not needed doesn't mean that it's wrong. Maybe this sentence has been used in a conversation in which it makes more sense to emphasize the pronoun.

[sailorcire]

What is the difference between czapka and kapelusz?

[Jellei]

"kapelusz" has a brim. It can for example be a straw hat, or a top hat, or a fedora.

The most common types of "czapka" are a baseball cap/hat or a winter beanie.

The only problem with distinguishing those is that English can use "hat" for both of those completely different things.