The word "faulty" was used all over this course, last time I checked. So, another thing to report wherever you can, please.
The word "rossz" can be used for all the above, bad, defective, broken, etc. And yes, sometimes it can be used for "not the right one" or "the wrong one".
"Rossz kulcsot hoztam." - I brought the wrong key.
There are more specific words for broken, faulty, broken down:
"hibás" - with fault, at fault, defective
"törött" - actually broken (into pieces)
"elromlott" - broken down
No you wouldn't. A native speaker wold say "These keys don't work." Faulty is usually used in reference to complicated electronic or mechanical equipment or something else technical. It collocates to, "machine" "engine" "structure" and "mechanical". https://www.ozdic.com/collocation-dictionary/faulty
Some dictionaries are more encompassing. Also, many keys are fairly complicated these days! For example, many cars can be opened, started, operated, etc, without ever taking the key out of the pocket... For another accepted reference, see: https://en.oxforddictionaries.com/definition/faulty
Googling would be great (18K+ hits on "faulty key"), BUT I would settle on Oxford Dictionary's 1st entry and several of the examples referred to, such as: "faulty wires," "faulty brakes" and "faulty light bulbs." Yes, I know how complicated brakes can get... NOW, if you really want to get complex, search for "faulty encryption key" (without the quotes) and you will get quite a plethora of usages related to faulty keys, related to encryption processes... I wish you the best.
"faulty car keys" with quotes 90 non-duplicate results
"bad car keys" with quotes 60 non-duplicate results
I added "car" because there are too many unrelated uses of the word "key" to make the exercise meaningful.
"faulty house keys" 1 relevant result "bad house keys" 0 relevant results
If one wants to descend to the nitty-gritty, this Hungarian sentence is about keys only; there aren't necessarily any relevant locks. It could be said about keys that had been produced (perhaps complicated, electronic car keys like ID-007 pointed out) that did not meet some technical specification and therefore are destined for the scrap heap, whether or not they could actually unlock locks. Obviously, I hardly object if they decide to accept "These keys don't work"; for all I know they already have.
If I come across a thread where you object to faulty kindergarten teachers, I will upvote :)
"faulty car keys" with quotes 3,660 results
"bad car keys" with quotes 19,200 results
"bad car keys" without quotes 13,200,000 results
I guess you could chalk this up to a British vs. American English. Except, nothing in this sentence but the mistranslation of the word 'rossz' would suggest the use of car keys in a particular lexical chunk. Since, 'rossz' appears as 'faulty' all over the lesson, we might as well be arguing if you can call your dog 'faulty', your breakfast 'faulty', or your kindergarten teacher.