I see you're really looking for some feedback, so here is my penny worth: it's probably older version BT in your car, that could be a problem, since phone has latest one and streams nice at least to my BT headphones, for example. My car is 6yrs old and I don't even have streaming option, at least none that I can find or make it work. If I was you I could probably try to see if I could get updated software for the radio, either from the dealer if factory, or from manufacturer if aftermarket set. I know my Toyota had at least 3-4 software updates, mostly maps, but also programing. But I don't care, calling over BT works, otherwise I listen to the car radio, cut CD to use in the player, or hook up wire to aux input. I know this is not exactly what you're looking for, but without knowing any details about your car, I can't even point you out to proper car forum, where other people could have similar problem with different phones and already found solution.
BTW your English is fine, no reason to be sorry.