I've been playing a trickster rogue, I do a ton of damage but I can barely take any, so there is a lot of tricky maneuvering. I like it a lot.
1. Skirmishes are PvE. Basically a group against several waves of enemies, and a boss or several mini-bosses. It's worth queuing for them, especially if you do dailies.
Coincidentally, PVP is actually really fun in Neverwinter, and I generally hate PVP.
2. Yes, Foundry quests scale to the level of the person entering them. Most of them are doable solo.
3. Regular quests? I don't know for sure. I haven't tried to do a quest that was over my head, either solo or with a group.
4. I haven't gotten to max level yet, but I'm about level 40 and from what I can tell, you generally don't have to do repeatable quests to level up. There ARE some repeatable quests, and there are daily tasks (dungeon runs, skirmish, PVP, foundry) that are worth doing for Astral Diamonds, and you gain levels pretty quickly from those.
5. There are group queues, where you sign up and it will automatically form a team for you to do dungeons or skirmishes. However, these only allow you to queue for dungeons at your level, so if you're higher/lower than the recommended level for a dungeon or skirmish, you're restricted to using the zone chat to go 'Lfg for skirmish!'
6. I heard you can get special mounts or loot rewards from building a popular Foundry dungeon, but I don't know for sure. If people like your dungeon, they're asked if they want to leave a tip of Astral Diamonds. I always leave tips at dungeons I enjoyed.
For a free game, I honestly think it's really nice. There is a currency that you can buy with real money, but anything that uses that currency is attainable via grinding, which I like - you can either invest time or money, but you dont have to do both. I look forward to there being a bigger RP community setting up in game, myself. I love RPing and I miss doing so in an MMO setting.