Learn Polish: Ile zarabia ten taksówkarz? - How much does this taxi driver earn?

It is built from the base noun taksówka (taxi). You drop the feminine ending -a and add the suffix -arz, which is the most common Polish suffix for deriving professions or doers of an action, much like the English suffix -er.

What is the feminine form for a female taxi driver?

You replace the masculine agent suffix -arz with its feminine equivalent -arka, giving you taksówkarka. You might also occasionally hear pani taksówkarz, but the derived form taksówkarka is very common and completely standard.

Why is the imperfective verb zarabia used here instead of its perfective pair zarobi?

The imperfective is used because this asks about a general, ongoing routine: what he earns regularly. If you used the perfective zarobi, it would shift the meaning to the future tense and focus on a specific completed result, meaning How much will this taxi driver earn on this specific trip or shift?

Is the word order strictly fixed, or could I say Ile ten taksówkarz zarabia?

You absolutely can say that, and it is completely correct. However, placing the verb immediately after the question word (Ile zarabia...) is the most typical and fluid word order for questions in Polish.