Answer 1: Your assumption is correct!
Answer 2: It's past perfect continuous.
To use past perfect continuous, try to understand past prefect first.
We use past perfect to show that the event occurred before something happened in the past. Here, they went missing, but if you want to show that 'missing' happened before her coming (which is also in the past), we use exactly the way you have quoted the sentence. We may call it as an 'early past'.
When she returned home.... her husband and daughter had been missing.
I'm pasting a useful portion from the British Council page for learning English.
Let's see two sentences
Both actions happened in the past, so we use the past simple tense. But look at how we can combine the sentences:
Mary rang John’s doorbell at 8:15 yesterday, but John had already left the house.
We use the past perfect (had left) because the action happened before another action in the past (Mary rang the doorbell).
Look at some more examples of the past perfect:
When Mrs Brown opened the washing machine, she realised she had washed the cat.
I got a letter from Jim last week. We’d been at school together, but we’d lost touch with each other.
The past perfect is used because they were at school before he received the letter. It refers to an earlier past.
Past perfect continuous just adds '-ing' verb to the past perfect. More on this topic here.