"would rather" and "would prefer" (wuld wrader and wuld prefer) = las dos frases significan "preferirían", pero su usan de forma diferente en una oración.
Ex:
I would rather go to the cinema than go to dance.
I would prefer going to the cinema than going to dance.

"would mind" (wuld maind) (importaría?) = se usa de forma directa e indirecta para preguntar si a alguien no le importaría o molestaría que realizáramos una acción.

Ex:
Forma directa:

You said)       would you mind doing exercise after eating?
                     (¿le importaría hacer ejercicio después de comer?)

Another person told you) yes, I would mind (si, me importaría) = I canot do it.
Or the same person told you) no, I wouldn´t mind (no, no me importaría) = I can do it.

Forma indirecta:

You said)        would you mind if I went to the bathroom?
                             (¿le importaría si yo fuera al baño?)

Another person told you) yes, I would mind (si, me importaría) = you canot do it.
Or the same person told you) no, wouldn´t mind (no, no me importaría) = you can do it.