Driving from Hungary to the Adriatic you enter Slovenia at Pince and continue on the A5 and A1. Regulated Slovenian off-motorway prices are usually below the Hungarian market prices that apply to foreign drivers. Refuel just after the border, around Murska Sobota or Maribor.
For foreign drivers usually yes — regulated Slovenian prices are below Hungarian market prices and often below Croatian ones too.
Yes. The Hungarian matrica is not valid in Slovenia; a separate Slovenian e-vignette is required.
Towards the Adriatic around Postojna or Koper; towards Zagreb in Novo mesto.