In a online game, is it considered good etiquette to offer a draw when the opponent obviously misclicked? For example, instead of capturing (and therefore exchanging) the queen on d8, white moved his queen from d1 to d7, and black can capture this queen for free. This is very likely the result of a misclick by white. Another example is moving the king for no reason in the opening stage. In this case, is it considered good etiquette for black to offer the draw, instead of taking advantage of white's misclick?

Some possible exceptions: 


My position is already winning before my opponent's misclick.
My position is still losing even after my opponent's misclick.
My opponent made a blunder which does not seem to be a  misclick.
My opponent demonstrated bad sportsmanship before misclicking.


In all above four cases, I will not offer draw.
Just to offer a different answer: 

No. No takebacks, no draw offers. In short time controls this is part of the game. It's the same as a blunder under pressure. I pressured the opponent on either time or position, and the person cracked and made a mistake.

Or your other example, of moving the king instead of castling in the beginning: That's what one get for trying to blitz out moves. Might save you a second here and there, but the risk is these mis-clicks. That's a price my opponent will have to pay, can't have the cake and eat it too.

(For longer time controls (1h+) I might think trying to salvage the game is the right choice, but I only really play 5min and below)