Drawing from the top might be your best bet. I have also drawn from the tap on my bucket and it has never hurt anything. To be honest, I don't bag it, though I will swab it with some no-rinse if I think about it.
However, I always just remove the lid on my bucket and drop the sanitized hydrometer in...that's easiest for me.
You should transfer your lager to the secondary once primary fermentation stops, i.e., you've reached your FG, pretty much the same as an ale.