Third person "having things done for oneself"

Question

Can you guys give us a full breakdown of what things (verbs) use the third person "they did this for me" but it's translated in English as "I had done." ?? It's very confusing and it seems kinda random what things you can use this with or not. The only reason I even knew that this structure existed is because I have some Mexican family members who use this structure but in English. For instance they might they "they're fixing the car right now." But they mean they're having the car fixed for them right now.

In some lessons you guys mention personal care "being done for oneself" but it's still first person, like cutting hair, doing nails. I'm just confused as to when it's ok to use third person or not.

Answer

Hola A
The structure explained in this lesson is used more generally than in the situations explained in the other lesson you mention about beauty/hygiene. 
As we explain in the lesson on beauty/hygiene context, the most common/preferred structure is the one that uses a reflexive verb:
Me he cortado el pelo. 
I've had my hair cut. 
We keep on explaining in that lesson about beauty context that you can actually also use:
Me han cortado el pelo. (not reflexive, but the they form "han cortado")
But this would be less used than the previous structure: Me he cortado el pelo. (meaning that you had it done, not that you cut it yourself)
In this other lesson, where we don't mention so much beauty/hygiene context, where we explain the they form structure, for example:
Le han diseñado el traje a su gusto.
She had her outfit designed the way she wanted it.
we can't say exactly in which specific context we use this because it does vary; we do say however that it is common to find it in sentences with a negative connotation, for example:
Nos han quitado nuestros juguetes.
We had our toys taken away.
We can't specify any more because it'd be wrong to talk about one specific situation. 
Saludos
Inma