1.) You can keep on grinding. You can even switch classes/jobs and you will still be que'd as the class or job you originally registered for under the duty finder (as long as you switch back). If you join a party or initiate a leve you will be kicked out of Duty Finder.

2.) For trash mobs don't try to pick up and kill all the adds. The tank needs to gain enmity on them and they will need to be slept by a mage. The only time I would engage trash mobs is to Shadowbind them when I see them going for the mage, but don't dps it. Always stay on the same target as the tank. The only adds you should be picking up are specific boss adds like the feathers on Garuda or something, but that should be discussed with your party. Even though there are groups of mobs we engage mob mechanics are still just like FFXI for the most part. Instead of pulling them one at a time we are just pulling a group, sleeping them, and killing them one at a time. Same process just a different coat of paint.