Firstly: a mí and yo are not interchangeable. I would like to see the websites that claim that.
The word «mí» means “me” when preceded by a preposition (except «con» which becomes ̣_«conmigo»_), so «a mí» means “to me”. When use as indirect object usually the first person will use the non-prepositional object pronoun «me». Compare:
«Juan le dio la carta a María.» “John gave Mary the letter.”
«Juan me dio la carta.» “John gave me the letter.”
For emphasis some times this indirect «me» is complemented by the prepositional phrase «a mí»:
«Juan me dio a mí la carta.» “John gave me the letter.”
In Spanish when referring to people, the direct object usually take the form of an indirect object, adding preposition «a». this is know as personal «a».
«Juan recibe un pedido.» “John takes an order.”
«Juan recibe a María.» “John takes Mary.”
«Juan me recibe.» “John takes me.”
«Juan me recibe a mí.» “John takes me.”
So «a mí» is just an emphatic form of the first person pronoun in objects (direct or indirect objects). While «yo» is the (emphatic) first person pronoun in subjects.
«Le dí la carta a María.» “I gave Mary the letter.”
«Yo se la dí.» “I gave it to her.”
«Recibo un pedido.» “I take and order.”
«Yo recibo un pedido.» “I take and order.”
Now, where is your conflict:
«A mí me gusta el chocolate.» “I like chocolate.”
«Yo amo el chocolate.» “I love chocolate.”
As well as the non-emphatic forms:
«Me gusta el chocolate.» “I like chocolate.”
«Amo el chocolate.» “I love chocolate.”
Unlike «amar», which works as English “to love”, the verb «gustar» is different. While usually translates in sentences as “to like” it actually behaves more as “to please”: the subject is what is liked (what pleases), and the object is who likes (to whom it pleases). So «me» and «a mí me» is the object, while «el chocolate» is the subject in «A mí me gusta el chocolate.»
Also in:
«Me gusta María.» “I like Mary.”
Note that «María» takes no personal «a», because «María» is the subject, not the direct object.
Your second confusion: interchangeability of «A mí también» and «Yo también.»
— «Ayer fuí al cine.» “Yesterday I went to the movies.”
— «Yo también.» “So did I.”
— «Juan me invitó.» “John invited me.”
— «A mí también.» “Me too.”
— «Amo el cine.» “I love the movies.”
— «Yo también.» “So do I.”
— «Me gustó la película.» “I liked the picture.”
— «A mí también.» “Me too.”
As you can notice, «Yo también» is used when it should be a subject and «A mí también» is used when it should be an object.
"mí" means "me" and "yo" means "I"
That's a good first approximation, if not the whole picture.