Question

Diana prefiere que nosotros ____ (tragar) la comida para las vacaciones

Answer 1

It would be "Diana prefiere que nosotros tragamos la comida para las vacaciones" because you have to conjugate the verb "tragar" for Nosotros, so you would replace the "-AR" ending with "Amos".

Answer 2

Is this about subjunctive mood? If so then the answer would be traigamos. In the subjunctive form, irregular yo forms carry throughout all forms including nosotros.