She wishes she was a dancer.

He wishes he had never bought that car.

She wishes she was a dancer.

 Dansçı olmayı  istiyor. [isterdi]

================

He wishes he had never bought that car

 O arabayı hiç almamış olmayı diliyor. [dilerdi, isterdi]

But  more everyday Turkish  for your sentences would be ;

She wishes she was a dancer.

 Keşke bir dansçı olsam diyor.

================

He wishes he had never bought that car

[Keşke] O arabayı hiç almasaydım diyor. 

[ Keşke] O arabayı hiç almamış olsaydım diyor.

Foxy. Thank you, tunci.