Learn Croatian: Imamo li majoneze u hladnjaku? - Do we have any mayonnaise in the fridge?

Majoneze is in the genitive case, not the accusative. In Croatian, when you are talking about an unspecified amount of an uncountable noun (like "some" or "any" mayonnaise), you use the genitive case without any extra words. This is called the partitive genitive. If you used the accusative majonezu, it would mean you are asking about a specific, whole unit, like "the mayonnaise".

Could we just say Da li imamo majoneze instead of Imamo li majoneze?

Yes, you can. Da li imamo is very common in everyday spoken Croatian. However, putting the verb first followed by the particle li (Imamo li) is considered the standard, more formal way to ask a yes/no question in writing. Both mean the exact same thing.

Why is it u hladnjaku instead of u hladnjak?

The preposition u can take either the accusative or the locative case. You use the locative case (hladnjaku) to show static location, meaning the mayonnaise is resting inside the fridge. You would use the accusative (hladnjak) for motion or direction, like if you were actively putting the mayonnaise into the fridge.

I've also heard the word frižider. Is that the same as hladnjak?