I have never seen a healthy reef tank without Bristle Worms.  They are almost always good.  There are occasions where you get a large bristle worm that can cause problems, but this rarely happens.  Even some of the very large ones are harmless detritus eaters. 

 

It is possible to get a larger than wanted population of them (unsightly), but they can easily be reduced by placing a piece of shrimp (or other type of fishy food) wrapped in some bridal veil in your tank at night.  Wait a few hours and then remove the shrimp/bridal veil with the attached worms.  I have never had to do this, but I know others that have.  If you do have a huge population this is usually a sign that you are overfeeding your aquarium.

 

Bottom line is I wouldn't worry about this guy.  It is usually a sign of a healthy aquarium.  They eat detritus and help clean your tank. I wouldn't medicate your tank because of them (EVER), and I wouldn't worry about getting a wrasse or other type of critter to eat them.

Predators are a very effective way of keeping a population in check but careful here- most Wrasse who will actually and reliably chomp them also enjoy other treats such as shrimp......  which can get expensive.

6/7 line are a toss up, if you read a lot about them you will find that some will eat them, some will not... but they all have the possibility of turning into a terror when they get bigger, as do most predators.

 

They do, they just seem to not last very long, and don't like living with other shrimp.