dirigirse - seems to have a wide range of English translations

Question

I am trying to get a understanding of this verb -- it seems to be very useful.

1. Fred, Daphne y Velma se dirigieron hacia el plató, mientras Shaggy y Scooby fueron a buscar rosquillas.
   (Fred, Daphne and Velma headed toward the set, while Shaggy and Scooby went to look for donuts.)

se dirigieron = directed themselves (I am using "headed") I'll bet the use of "headed" is a problem for students learning English. .... also of interest is "fueron" here I believe it is a conjugation of "ir" because of "a buscar"; if "fueron" is a conjugation of "ser" the translation would be "were looking for donuts" which I believe is incorrect.
Am I right or wrong?

1. -Mírala - dijo, sin dirigirse a nadie en especial -, Angela tiene un aspecto ridiculo con ese traje.
   ("Look at her" she said, without speaking to anyone in particular, "Angela looks ridiculous with that outfit".)

sin dirigirse = without addressing/directing (I am using "without speaking ")

Are my translations of "dirigirse" correct or to far from the literal translations'

Answer 1

One of the meanings of "dirigir" as a transitive verb, is to make something or someone the destination or recipient of something or someone. E.g. dirigir unas palabras a alguien, dirigir a alguien a un lugar, dirigir una carta a alguien,... Its pronominal counterpart removes the thing or person that has to reach its destination, because that person or thing to be directed is the subject of the sentence or belongs to this person, i.e. it makes the verb intransitive, removing one of the arguments. So you have "dirigirse a alguien" (address someone) and "dirigirse a un lugar" (head for). If the destination is a place, you "send your own body there", and if it is a person, you "send your words there" (I'm being deliberately and exaggeratedly literal here; obviously it doesn't sound like that to use either). Objects can also use this verb: "El misil se dirige hacia el objetivo".

Notice that when you address someone, you letters or words are "directed" towards this person.

Answer 2

The first sentence I believe is totally correct.
The answer is yes, you are right.

Answer 3

1. -Mírala - dijo, sin dirigirse a nadie en especial -, Angela tiene un aspecto ridiculo con ese traje.

('Look at her? she said, without speaking to anyone in particular, 'Angela looks ridiculous with that outfit'.)

sin dirigirse = without addressing/directing (I am using 'without speaking ')

you can also say: ...sin dirigirse a nadie en particular...

you are not using without speaking, you are using without addessing, but everything is correct.