The use of prepositions has to be learnt. It's tedious, but there's no way around it.
When I learned English, I was given long lists "to think of, to concentrate on, to insist on..." In German, "to think of" is "denken an".
Not entirely sure whether it is an accepted variant and please correct me if I'm wrong, but isn't "we think on" an accepted variant in Scottish English?
As an example, from Tam O' Shanter, by Robert Burns
"We think na on the lang Scots miles, The mosses, waters, slaps and stiles, "
Regardless of whether's it's correct or not it's still cool to see similiarities between English and German in older works!
No, the "an" is a preposition and therefore must come immediately in front of the things (or persons) referred to. It doesn't make sense at the end of the sentence with nothing following.
This is a different situation than e.g. in "ich schalte das Licht an", where the "an" is a part of the soplittable verb "anschalten" and not a preposition.
"We think about our families." should be accepted.
Do you suggest that it is not accepted now? It was definitely accepted about 2 years ago, as also noted in this very discussion https://forum.duolingo.com/comment/11026163?comment_id=29015377