Learn Turkish: Gelecek hafta yeni bir elektrikli araba alıyorum. - Next week I am buying a new electric car.

In Turkish, the indefinite article bir (a/an) usually goes between the adjective and the noun. So "a new car" is yeni bir araba. Here, elektrikli araba (electric car) acts as a single noun concept, so bir comes right before it, giving us yeni bir elektrikli araba.

The sentence talks about gelecek hafta (next week). Why does it use the present continuous verb alıyorum instead of the future tense?

Just like in English ("I am buying a car next week"), Turkish often uses the present continuous (-ıyor) for future events that are already planned or arranged. You could also say alacağım (I will buy), but alıyorum sounds perfectly natural for a set plan.

Since we are currently learning about ne kadar (how much / how long), how would I use it to ask the price of this car?

You would simply say: Yeni elektrikli araba ne kadar? (How much is the new electric car?). To ask a price, you just put the item you are asking about before ne kadar.

Does gelecek in gelecek hafta just mean "next"?

It translates to "next", but structurally it is the future form of the verb gelmek (to come). So gelecek hafta literally means "the week that will come". This is the standard way to talk about the upcoming week, month, or year in Turkish.