No it isn't bad, not at all. I wish there was a "back burner" type of status on there that you could enact without the other person knowing.
The lyrics to "Engel" and "Du Hast" are pretty tame.
Depends on how you take it. "Hast" means have, but if you spell it "hasst" it's hate. Both meanings work, because the song pretty much bashes marriage. I spent like 2 hours reading up the translations to their discography. They're really good, but really messed up. This is part of a song, I forget which:
"He met a girl that was blind
Shared pain and like-minded
Saw a star go from the sky
And wished that she could see
She opened her eyes
And left him in the same night"