Learn Turkish: Adam araba sürüyorken polis ehliyet istedi. - The police asked for his license while the man was driving.

It combines the root verb sür (drive) with the present continuous suffix -üyor (is driving) and the conjunction -ken (while). Notice that even though the main action happened in the past (istedi), we use the present continuous before -ken to show that the driving was an ongoing background action when the police stopped him.

How do we know who is driving if sürüyorken doesn't have a personal ending?

The suffix -ken is frozen and never takes personal endings like -um (I) or -sun (you). We know who is doing the action by looking at the subject of that specific clause, which here is Adam (the man).

Why are the words araba (car) and ehliyet (license) missing the accusative case endings?

They are general, nonspecific objects. The man isn't driving a specific car we've talked about before; he is just doing the general action of 'car-driving' (araba sürüyor). The same goes for the license. When a direct object is general and placed right before the verb, it drops the accusative case ending.

I learned that istedi means 'wanted'. Why does the English translation say the police 'asked for' his license?

The verb istemek literally means 'to want.' However, in Turkish, expressing that you 'want' an item from someone is the standard, natural way to say that you 'asked for' it.