Hola Nicole,

¡Feliz Año Nuevo a ti también!

En referencia a tus preguntas:

1. Me recuerda al roscón de reyes (It reminds me of King Cake.)

The way this is used in Spanish and in English is different. In Spanish we say "(Algo) recuerda a alguien a algo". But in English it is "Something (it, that...) reminds someone of something. I´ll explain:

"Me recuerda al roscón de reyes." 

Here the subject is omitted, but it refers to the dessert the exercise is talking about "The Easter cake. So there is no explicit subject in the sentence as this is understood. That would be the English "It" as you can see in the English translation "It reminds me ...". If we include it in the Spanish sentence it would say: "La mona de Pascua me recuerda al rosco de reyes." The verb recordar is agreeing with the subject "La mona de Pascua me recuerda"

2. It does indeed work similary to "me gusta" in the sense that it is using the pronouns to express the indirect object which is the person who is doing the "remembering" (or the liking with gustar). For example:

Nos gusta el café. (The coffe pleases us [We like coffee])

Nos recuerda a nuestra prima. ([That lady] reminds us of our cousin)

3. As mentioned before, in Spanish the preposition "a" is used while in English "de [of]" is used. It is as if we said in Spanish "it reminds me TO something", or "it brings my memory TO something" (if you know what I mean)

With reference to the use of "ser" not estar here:

"porque su forma es similar/  parecida"

We are simply describing with an adjective. It is not referring to a result of something, in which case we'd use estar. The shape of that dessert is [always] similar to the shape of the King Cake.

I hope this clarified your doubts.

Noted a lesson on "how to say to remind of something in Spanish". There is nothing reflecting this at the moment. Thanks for reminding us : )

Inma