Learn Finnish: Minulla ei ole mitään.

Finnish doesn't have a direct verb for 'to have'. Instead, it expresses possession by saying something is 'on' someone. We use the adessive case suffix -lla on the pronoun (minulla means 'on me') followed by the verb 'to be'. To say you don't have something, use ei ole (is not). So, minulla ei ole literally means 'on me is not'.

Why is it ei ole instead of en ole since the English translation starts with 'I'?

In possession sentences, the person who owns the thing is not the grammatical subject! Because of this, the verb 'to be' is always fixed in the third-person singular form on (is) or ei ole (is not). It never changes to match the owner, so you never say minulla en ole.

Why is the word for 'anything' written as mitään instead of its base form mikään?

As this lesson teaches, in negative possession sentences the thing you do not have must be put into the partitive case. Mitään is the partitive form of the pronoun mikään.

If mitään means 'anything', how do you translate 'I have nothing'?

This sentence is exactly how you say 'I have nothing'! In Finnish, you cannot use a word for 'nothing' with a positive verb. You must use the negative verb ei ole paired with mitään to express 'not anything' or 'nothing'.