Translation:My parents do not like walking at night.
When you say something like "me gusta" or "te gusta", it's very obvious who it's about. "I like" or "you like", respectively, and you don't need to add the subject of the sentence.
However, when you get to "le gusta" or "les gusta", the subject isn't always easily inferred. So when you add a subject, that's where the "a mis padres" comes from.
A él le gusta = he likes. A mis padres les gusta = my parents like. A usted le gusta = you like.
Sometimes the subject was mentioned in a previous sentence, and you can leave out the "a mis padres" because it's able to be inferred due to context: "Mis padres se van de vacaciones. Les gusta viajar a México."
Are "en las noches" and "en la noche" interchangeable? I ask because in this same unit, I just had another example where they used the plural "en las noches" form and the translation is exactly the same, so obviously this is idiomatic in some way, but is there a clue as to when one is preferred or are they completely interchangeable?
"gusta" is conjugated accordingly to what is being liked:
When you like a single object ("la casa" for instance):
- a mi me gusta la casa
- a ti te gusta la casa
- a él le gusta la casa
- a nosotros nos gusta la casa
- a vosotros vos gusta la casa
- a ellos les gusta la casa
When you like a multiple objects ("los coches" for instance):
- a mi me gustan los coches
- a ti te gustan los coches
- a él le gustan los coches
- a nosotros nos gustan los coches
- a vosotros vos gustan los coches
- a ellos les gustan los coches
On the above examples, there are optional segments, for instance in "a mi me gusta la casa", "a mi" is optional.
Attention, when the "likeness" is towards someone there is an exception:
- yo me gusto (odd but possible)
- tú me gustas
- ella me gusta
- nosotros nos gustamos (not sure if I can say "nosotros me gustamos" as "I like ourselves")
- vosotoros me gustais
- ellos me gustan
I don't exactly know why the contraction of "do not" is considered incorrect.