"This hat is old."
Translation:Ten kapelusz jest stary.
Yes we've been told from the start of this lesson that cap is czapka and hat is capelusz. I will admit i mismatched the adjective and the noun ("ta kapelusz" instead of "ten kapelusz") and deservedly was marked wrong, but the correction changed the noun rather than the adjective. This is very confusing for a student.
Not a question, but more like a suggestion. I wish we didn't have to go to the discussion just to have the option for the pronunciation in the desktop version. Like, it would be nice if it gave you the correct pronunciation after you chose/wrote the answer instead of having to click on the discussion just to hear it pronounced correctly.
Yes. To me, "czapka" is mostly either czapka z daszkiem (a baseball cap or similar) or czapka zimowa (a beanie). At least from the ones in common use. A number of other, a lot less common usages you can find here if you click the links for different types.
As for "kapelusz", these examples I found may be too too much of "sunhats" indeed (edit: the pictures have been changed from that time). They definitely can be more elegant. I think what defines a kapelusz, is the fact that it has a brim. A top hat for example, is definitely a kapelusz, although it has it's own unique name - cylinder. Maybe you could have a look at Polish Wikipedia here, click some links the article lists and see what we consider to be a kapelusz :)