Yes. Preferir is an e → ie stem-changing verb in the present tense, except in the nosotros and vosotros forms.
Present tense:
So prefiere is the correct form for mi abuela.
Both verbs can relate to removing something, but quitar is very natural for taking away / removing an ingredient from a dish. In cooking, quitar el laurel sounds very normal: you put in the bay leaf for flavour, then remove it before serving.
Sacar usually focuses more on taking something out from inside somewhere. It is possible in some contexts, but quitar fits this sentence very well.
Because the full direct object is already stated: el laurel. Spanish does not need a pronoun if the noun is right there.
Both are grammatical, but if you already name the thing, the pronoun is not necessary.
After antes de, Spanish uses an infinitive when talking about an action in a general way, especially when the subject is the same or understood.
If Spanish needs a new subject and a full clause, it usually uses antes de que + subjunctive:
So antes de servir is exactly the normal structure here.
It is understood from the context, so Spanish leaves it unstated. In a cooking sentence like this, servir usually means serve the food / serve the dish / serve the meal.
Spanish often omits objects when they are obvious:
So antes de servir sounds complete even without saying exactly what is being served.
Spanish adverbs like siempre are quite flexible, but putting siempre before the verb is very common and natural:
You could also hear quita siempre el laurel, but that can sound a little more marked or emphatic depending on context. The version in the sentence is the most neutral one.
The present tense in Spanish is often used for habits and repeated actions, just like in English:
This tells us what she generally does, not just what she is doing right now. It is a habitual present.
Not necessarily. In Spanish, el laurel can refer to bay as an ingredient in a general sense, not only to one literal leaf. In cooking, though, it often does suggest the bay leaf that was added to the dish and then removed.
If you wanted to be very explicit about multiple leaves, you could say las hojas de laurel.