In case anyone wonders, the emphasis should be 'motórer', not 'mótorer' as the TTS suggests.
Do most loan words or words derived from other languages take "-er" in the plural?
I'd say they do. It's not a rule but if you have a loan word and you don't have a clue, go with -er. (This reminds me of the story my Russian teacher told me. When she went to the then Soviet Union for the first time and didn't know much Russian and couldn't always remember what ending a word would take, she'd just mumble something unclear. Works every time.)
That's one hell of a teacher. Did you get good grades for saying gibberish when you didn't know your lesson?
My teacher taught me that (most?) "internationella" en words take -er in the plural. Banan/bananer, biolog/biologer, restaurang/restauranger, etc.
No, sorry, but similar structured words usually take the same plurals. All words on -tion are en for example.
I am curious why motors is not accepted. At least in every day conversation engine and motor are equivalent.
Motors are machines. is another accepted answer. Could be some bug or glitch if you typed that and didn't get it accepted.
while engine and motor are interchangable in some cases, but not always. Is there a distinction between them in Swedish?
No, there isn't. In Swedish you specify different kinds by adjectives or composite words: "förbränningsmotor", "elmotor/elektrisk motor", and so on.