"Her shoes are white."
Translation:Hendes sko er hvide.
Because "sine" along with sin and sit can only be used on the object of a sentence. And can only be used if the object belongs to the subject if the subject is a third person, singular pronoun or noun. "Hun har sine hvide sko" (she has her own white shoes) is different to "Hun har hendes hvide sko" (she has her [someone else's] white shoes)
Well, in this sentence there is only a subject, and since "sin/sit/sine" only goes with an object it wouldn't be right to have it in this sentence. However, in a sentence like "She has her white shoes" both "Hun har sine hvide sko" and "Hun har hendes hvide sko" should be accepted, if not then report them
It depends on the noun it is describing.
Common gender (n-words) use the base-form without adding anything (In this case "Hvid")
Neuter gender (t-words) you add a T to the adjectives. (In this case "Hvidt")
Plurals, possessives (min, din, deres etc) and definites with a prepositioned definite markers (den, det) adds an E to the baseform. (In this case "Hvide")
Shoes - Sko (doesn't change form in plural) is a common gender plural which is why the adjective is in the e-form.