"I came to Japan last week."
は is used if the time expression is the topic of the sentence, the thing that is talked about. If the sentence was said in reply to the question "What did you do last week?", it would need a は, but if it was in reply to "Tell me something about yourself!", it should not have one (because "last week" is new information). Of course, Duoling never gives context, so both versions should probably be acceptable.
Oh, and another use for は is contrast -- if the sentence is in reply to the question "Terrible weather we had last month, wasn't it?", it should actually have a は even though "last week" is new information. But that is a special case.
from what I have read, being able to type in the app was a trial that Duolingo were running and the trial has now stopped (extremely frustrating!!).
To keep typing answers in Japanese, stop using the Android/iOS app and do the lessons in your phone's browser as the option to type answers is still available in the duolingo web app. I've tested it on Firefox, Chrome and the Samsung browser.
Why on earth is 先週日本へ来ました wrong? "友人のジョージがこの夏に日本へ来ます" is even an example sentence on https://context.reverso.net/translation/japanese-english/%E3%81%B8%E6%9D%A5