Hi @Martin.
No the Wall Charger does not come with the car. I you want a wall charger you would need to bye it privately.
It does come with two chargers. A Type 2 charger and a Three pin charger which can plug into a mains socket at home, the three pin plug charger will only charge your car at 1.3 Kwh whereas the Type 2 will charge at 7 kwh.
No a Tucson Phev cannot use fast charge ports as the most it can charge at is 7 Kwh. I have a Tucson Phev Ultimate, it will take me approximately 2 hours to charge with a Type 2 charger.
Various people with PHEV’s on the forum have not bothered with a wall charger and just used the 3 pin charger. Others do not like the idea of the 3 pin charger being plugged into the mains for such a long time so have paid for a wall charger.
I have had my Tucson PHEV since April and have found it a wonderful car.
If you have any questions please don’t hesitate to ask.