German divides things up a bit differently than English :)
"Burg" is a castle (fortified place). "Schloss" can either be a castle or a palace, but is usually less strong/defensive than a Burg, I think. "Palast" can only be a palace.
I'm not sure whether every "Palast" can be a "Schloss". Certainly not every "Burg" would be a "Schloss".
I guess that the main point of a Palast is luxury; the main point of Schloss is that nobility live there (which sometimes needs a bit of strong masonry to protect them, depending on location); and the main point of Burg is the defence.
So if an army garrison is stationed there, it won't be a Schloss but has to be a Burg, while a similar building housing a local lord instead could be a Schloss.
There's also the French loanword "Palais" but I'm not sure exactly where that fits in.
I never got an email saying that I would get a reply, but I did have a couple where they said they had made a change. I suspect that a lot of people had reported the same things. And I have reported a lot of other things that I have never had a response on. I think part of the problem is that they will fix it only on the reported exercise, but it will still exist in other exercises.
Yes, Schloss means not only a castle but also a lock as in the lock on a door or a padlock (which is more specifically a Vorhängeschloss).
"to lock" as in the verb is abschließen -- in the simple past tense, it looks a lot more similar to the noun, e.g. Ich schloss mein Auto ab "I locked my car". (Though you'd probably hear the compound past more often: Ich habe mein Auto abgeschlossen.)
It's not a lock as in a lock in a river, though (for ships to go up or down), or an airlock. Those are eine Schleuse (airlock: Luftschleuse).
About "schön". Way back. I learnt schön = beautiful/handsome, hübsch = pretty & nett = nice. I also got tired of typing beautiful and typed "This castle is handsome". I was wrong. I can wear that; but I got "This castle is nice" as the accepted translation. I would never translate schön as nice. Am I wrong and out of date?
"This castle is beautiful" is a good translation and is the default translation.
Additional accepted translations are unfortunately not always completely uniform across the course and may depend on the person who added them and/or on what people had suggested as alternative translations.
The equivalences you learned are good (though I would personally use gutaussehend "handsome" for a man rather than schön "beautiful"), and "nice" is not a very good translation for schön.
Calling it "the accepted translation" is misleading; it's not the only accepted translation nor the one that's considered best. It may be "an accepted translation" as sometimes the course is a bit lenient in what it accepts -- sometimes more, sometimes less.
That was a very unhelpful response. Why respond if you don't mean to be helpful? My point is that lock is a correct response, and not so ridiculous as to be marked incorrect. It was not out of context and as a locksmith myself I have crafted many beautiful locks. Surely language learning is the goal of this course and not unhelpful opinions.