Learn Finnish: Naisella ei ole kuittia. - The woman does not have a receipt.

Words ending in -nen usually change the -nen to -se- before adding an ending. So, nainen becomes the stem naise-. Then we add the -lla ending to indicate who has something (literally "on the woman").

Why does the sentence use ole instead of on?

When you say someone has something, you use on (for example, Naisella on...). But to say someone does not have something, the verb changes to ei ole. The word ei does the negating, and ole is the special form of the "to be" verb used right after it.

Why is the word for receipt kuittia instead of the dictionary form kuitti?

Because the woman does not have it! In Finnish, when you state that someone does not have something, the thing they are lacking must be put into the partitive case. Here, we add the partitive ending -a to kuitti to get kuittia.

Is the word order strictly fixed for this type of sentence?