In what circumstance would one say 'Prowadzę samochód' instead of 'jadę samochódem' ?
where the fact you are driving is important. ex I cannot drink today, I cannot talk on mobile now, telling someone you want to drive today.
It kind of is not in Polish. ( It is more I am in charge, I am leading). Also not all verbs of motion have the go/is going distinction.
I can only remember 6:
go/walk - iść/chodzić
run - biec/biegać
go/ride/drive - jechać/jeździć
swim/sail/go - płynąć/pływać
fly/go - lecieć/latać
carry - nieść/nosić
"Drive" used to have the exact same meaning in English, too - driving your enemies before you, driving your oxes back to the barn...
Even then it is more like jeść/jadać(eat) pić/pijać(drink) spać/sypiać (sleep) siadzieć/siadywać(sit) widzieć/widywać(see) (one for both meanings other specifically for repeated action, rarely used)
If "a driver"="kierowca", it looks logical, that "to drive a car" might be translated as "kierować samochódem", doesn't it?
It's logicall and used in practice but rather formal (the police likes to use it). Normally we either „jechać samochodem” (no difference between passanger and driver) or "prowadzić samochód" (lit. to guide/drive/lead/conduct a car). Polish law uses „kierowca” for everyone that has driving licence whereas „kierujący” is the actual driver in the process of driving.
"jeżdżę" does not work for Present Continuous, unless you're just 'driving around' without any purpose and direction. It also doesn't really mean that I am driving, although it can. Basically it's a habitual form of "to go" (by vehicle).
"prowadzę" definitely means that I am driving, works both for Present Simple and Present Continuous, just as most verbs.