Due to can mean because of or caused by as you said, but in this context, it means expected or arranged to happen at a particular time (See Sense 2 of due on the OALD).
Therefore, "It was due to return later on Tuesday if weather conditions permitted" basically means the same as "It was expected to return ..."
Note that if has a lot of different uses, and the uses don't need to be one of the 3 (or 4, or 5, or more) types of conditionals you have learnt. If is usually used to give a condition, and here the condition is the weather.
As you know, we use the second and the third conditionals to talk about an 'unreal' (hypothetical, untrue, imaginary etc) situation. The second for the present, the third for the past.
Here, since nobody could really tell whether the weather would be good enough for the robot to return at the time the author wrote the news, the author simply used if to give a condition and used the same tense as other sentences, which is the past tense, in this news.
He or she wasn't talking about an imagined scene, so there was no need to change to tense to be more past as in the second or the third conditional.
Possibly the best way to explain is with some practical examples:
Before I could warn him that the floor was wet, John went rushing off down the corridor and slipped over.
As soon as he heard that there were fresh doughnuts in the canteen, John went rushing off down the corridor to get some.
The phrase 'Hurried away' is generally interchangeable.
EDIT
In this context, down is the direction that John went. It's commonly used in English but ambiguous - you could, just as easily, have used 'up' or 'along'.
To 'rush off' is a phrasal verb meaning to hurry away.
Just to confuse things even further for the unfortunate learner, there is an alternative meaning for the phrasal verb 'rush off' meaning to be busy - I'm rushed off my feet today
Best Answer
Eton is a prestigious British public school for boys. As an aside - in the British education system, a public school is a privately run school that people pay (large) fees to attend - normally a fairly old one. They're called 'public schools' because when they were established, schools were generally owned and operated by groups like the church or trade guilds, and they only educated their own members. Public Schools were open to anybody who could pay. A British public school is equivalent to a private school in the US; schools owned and operated by the government and free to all children are called state schools in the UK, public schools in the US.
Eton College is a particularly well-known and prestigious public school. Both of the current Prince of Wales's children, William and Harry, attended Eton; Nineteen of Britain's Prime Ministers have been Old Etonians; Foreign royal families have been sending their children to Eton for generations. Eton is also one of the most expensive Public Schools in Britain, currently charging about £39,000 per year.
Traditionally, parents would apply for their child's admission at the child's birth - that's no longer required, but it's still common for wealthy or prominent families to register their child early. Registration is commonly referred to as "putting one's name down" - not just in this context, but in any context. One might put their name down for the football team, for volunteer work, etc. It's a contraction of sorts, derived from "Putting (or writing) one's name down on a waiting list"
Justin Finch-Fletchley is saying that he is from a prominent and wealthy family - most likely minor aristocracy, going by his name - and that they had applied to Eton on his behalf when he was born, but he's more excited to be going to Hogwarts.