On that note, how does grouping up work, anyway?
Well there are quests that require more than one person (obviously lol), then you just type /invite [that persons name] and you're in a fellowship. So then you go into the instance or area to do the quest. You can be in a fellowship just to talk and still be able to do things as normal, you just can't enter solo only instances while in a fellowship. It's pretty easy, if you're looking for a quest to do then you just use the LFF chat or GLFF user chat and usually you will find people that will join you. It's LFF system isn't as awesome as DDO's and pretty much useless, only downer to grouping, but the LFF works just as well for most things, although it's not always fast getting a group.
To your edit: No you won't automatically receive the quest, you'd have to pick it up yourself, but it is possible for people in your group to share it with you and then the dialogue pop up appears on your screen. Once that happens, yes you can kill two and complete it while the other person does the same. The difficulty is already there, it doesn't increase or decrease with members in your group. If you try to solo a quest that has the fellowship symbol, then you will most likely die because the monsters are "elite" usually and a step up from normal monsters. The higher level you are the more stepped up they are, they change from elites to elite masters to nemesis and then to arch nemesis for your greatest enemies. As for Skirmishes, there's a solo mode and a mode for small fellowship (3 people), regular fellowship (6 people) or raid (12 people). And yeah the more people you have the harder it gets (3,6 or 12).
Also the starter instance and pretty much 95% of the quests in the starter areas are solo, so you won't find THAT much challenge there. It increases in challenge as you go on. Around level 20 or so you'll see more quests that have fellowship symbol and areas that have elite monsters. Doing the Great Barrow instance is one of these places.