I'm going to respond here to keep the input of others going; you've been given good advice from other very knowledgeable people so far.
Here's the list I was sent via PM:
Longfin Fairy Wrasse (Cirrhilabrus rubriventralis)
Whip Fin Fairy Wrasse (Cirrhilabrus filamentosus)
Pink Margin Fairy Wrasse (Cirrhilabrus rubrimarginatus)
Scott's Fairy Wrasse (Cirrhilabrus scottorum)
Carpenter's Flasher Wrasse (Paracheilinus carpenteri)
Linespot Flasher Wrasse (Paracheilinus lineopunctatus)
Filamented Flasher Wrasse (Paracheilinus filamentosus)
Blue Flasher Wrasse (Paracheilinus cyaneus)
Yup, just as you've been told, those two need to go away; quite aggressive with other wrasses. The rest should be fine together. These no real "number" or "limit" to how many wrasses you can keep together; it's all a matter of what species you're trying to mix and how large the system is.
Using an acclimation box on each new addition is very much encouraged as well. It helps nix most potential aggression before it happens.
Your tank MUST be covered with 1/4" mesh with ZERO gaps or holes. You'll need to feed ~3 times a day, offering a variety of meaty foods.