Why does Astrid say "well done" when killed?
This is highly speculative. I don't think there is an actual answer to this question.
However, I think it's simply because you did what she said. Loyalty means everything to the dark brotherhood, which is stated in a few books about the dark brotherhood. She said, that a "sacrifice would be required to join the dark brotherhood", so you have to kill somebody in the room, but who that somebody is, well, she left that choice to you. I think she thought about that risk, she wouldn't want to invite someone to the dark brotherhood who's stupid. She took the risk, got her ass whooped, yes, but you did the job, therefore she says "Well done".
On the other side, this is just my theory ... I mean, nobody could tell you where the dark brotherhood hideout was. Also, she loved the Dark Brotherhood, and she loved the leading position, so the death of her and her "family" surely wasn't her intention.
But as mentioned, there is no real answer to the question. However:
Most importantly, for my newly wed bride awaits me, is it safe to sleep?
Yes, it is. There won't appear any random assassins disturbing your honeymoon nights :P
I feel dirty posting a link to Yahoo answers, and in this case for good reason: this answer claims to have come from "Elder Scrolls Lore books" and yet none of the text garners a Google hit other than the answer on Yahoo answers itself:
"Astrid was allowed to join the Dark Brotherhood only once she had proven herself to show absolutely no emotions. To prove this, when Astrid was told to behead one of three criminals, of whose crimes she was told, she instead beheaded all three. Thinking this would prove of her emotionless personality, she returned to her recruiter and found him displeased." ...
"After some time her recruiter explained to her that she was being tested on whether or not she could discern who, in a group, deserved the most punishment. By beheading all of them, she had failed to set her own standards for what she herself considered punishable by death. This, in turn, showed that she used her emotion of desire and her need to please to direct her actions."...
"She would later use the same induction rite that she was given onto her new inductees. She would bring in three people that had committed different degree of crimes. However, she still found herself to have committed the greatest of crimes; she had used her own emotion to determine how she would pursue her directions."...
In summary, this is why she says "Well done." It is because the player, in her eyes, killed the person who had committed the greatest crime and deserved death over the others.
The uesp wiki's dark brotherhood lore book list contains no references to Astrid other than Cicero's Journal, which is unrelated to the text above. If anyone knows where one could find the text above I think it would help.
In the meantime this makes sense, but for all I know some guy on the Internet made it up.
Occam's razor; it was pretty obvious to me, at the time, that she was commending your combat prowess with her last breath.
You've just slain the leader of the Dark Brotherhood, arguably the most skilled assassin at the time... Well done.