Learn Finnish: Lompakko ei putoa tuolilta. - The wallet does not fall off the chair.

The ending -lta is the ablative case, which means from or off of an outer surface. Since the wallet is falling off the top of the chair, we use tuolilta. If it were falling out from inside something like a bag, you would use the -sta ending instead.

The dictionary says to fall is pudota. Why is it spelled with a t in ei putoa?

This happens because of a spelling rule called consonant gradation. To find the form used after the negative word ei, we use the verb's stem. For verbs ending in -ta/-tä like pudota, the weak d changes to a strong t in the stem, giving us putoa.

Why doesn't the verb putoa have a person ending here?

In Finnish negative sentences, the negative word ei does the heavy lifting. The main verb goes into a special base form that drops its personal ending entirely. The word ei already tells us it is third-person singular (it does not).

The lesson teaches keneltä for from who. How would I ask from what did it fall?

Since a chair is a thing and not a person, you would swap keneltä (from who) for miltä (from what). Both question words use that same ablative ending to show movement off of a surface.