What can I create with the GECK? Can I create quests, perks, weapons, armor, and characters? Can I create new levels to go to? Are there any mods that are like the DLC content for the game? What are some of the best/coolest mods?

What can you create? Just about anything. All the stuff you mentioned: quests, perks, weapons, armor, NPCs - you can make all that. You can add places to the Mojave or create your own wasteland and then shape it the way you want (that's very time consuming however).

There are countless mods out there but as for what's best/coolest, that's all subjective. Personally, I like (parts) of Project Nevada, Monster Mod, and A World of Pain. There are plenty of popular ones that I *don't* like but that's just because they don't fit my play style.