leenia, you're right. Goethe wrote "morgenschön", and that's how it's usually sung and printed. The "Google quota" is 45,900 : 4,470 in favour of morgenschön; a quota like this you may get for about any spelling error. Ingeb.org is mistaken.

The rape question has been discussed frequently. It is undisputed that the poem is about a love relationship with some component of violence, not necessarily physical. Many singers of Heinrich Werner's somewhat sentimental tune choose to ignore this fact willfully. Others, like Goethe himself, think that acts based on archaic emotions should not be measured in legal terms; the victims might disagree.

I know a woman who is "morning-beautiful": her wrinkles become more marked during the day, and when she has put on her evening makeup she's quite ugly; hardly a knave would rape her then ...