An 'epic' is an epic weapon that is quested for. It usually involves a long tortuous process, consisting of charging all over Norrath, chatting to NPC's who give you menial tasks to perform and various fights, some solo, some involving groups and usually at least one or two that need raid force. The end result is a cool weapon or weapons that unfortunately now are often not as good as some of the dropped weapons availiable.
AA's are alternative advancement points. When you get into the 50's, rather than have all your xp go into raising your lvl, you can choose to put some or all of the xp you gain into aa points. They are used to boost stats, or to give you entirely new skills. there is an ongoing debate about wether to gain levels first, or stop at a certain level and do aa's. I think most people do a bit of both. I tend to do aa's if I'm soloing. Makes it feel like your achieving something, as aa's tend to go faster than regular lvls.
Im assuming the crystals you are reffering to are the ones you get as a reward for completing DoN missions. These can be used to buy armour augmentations and weapons from certain merchants. Look
here. Theres Ebon ones too.
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"If you have selfish, ignorant citizens, you're gonna get selfish, ignorant leaders". Carlin.