Yes, it does have to be turned on to host a race. Your friends can host your drivers at any time even when your PS3 is turned off. You have to have set them online first though.
I'm not sure what other info you want. You can only put 1 of your drivers into a race that you are hosting. You can host all 6 of any friend's drivers, provided they have a high enough B-Spec level to own 6 drivers and have them all set to online.
