Learn Croatian: Imaš li plan? - Do you have a plan? informal

The verb Imaš already means you have (informal). In Croatian, the subject pronoun ti (you) is usually dropped because the ending of the verb makes it perfectly clear who is doing the action.

What is the purpose of the word li in this sentence?

The word li is a question particle used to turn a statement into a yes/no question. To ask a question this way, you put the verb first (Imaš), followed immediately by li.

The verb to have usually requires the accusative case. Why doesn't the word plan change its ending?

You are right that the object of imati takes the accusative case! However, plan is a masculine inanimate noun (it is a non-living thing). In Croatian, masculine inanimate nouns look exactly the same in the accusative case as they do in their basic dictionary form.

Is there another way to ask if someone has a plan in Croatian?

Yes! You will often hear people use Da li at the beginning of a question instead. You could ask Da li imaš plan? Both mean exactly the same thing, but the Imaš li... structure is considered a bit more standard in writing.