There are several parts to Catacombs.
1) Taskmaster instanced dungeons (TIDs): See your level-appropriate taskmaster and he will send you to a nearby instanced dungeon to either clear it, kill a named mob, or kill number of particular mobs. In the 1-10 TIDs, you get regular tattered armor drops and coin. In the higher dungeons, I think you just get coin. No other drops. For soloers, except for the 1-10 TIDs, where the mobs are blue fading to green as you approach level 10, the mobs will be yellow fading to blue in the higher level TIDs. This is not risky enough for a lot of players who enjoy taking on orange cons and higher. You can "fool" the taskmaster by grouping to get the dungeon and then going in alone. This might get you higher level mobs, but it might also get you multiple mobs on a pull, so be careful using this strategy.
2) Adventure Wing instanced dungeons (AWIDs). These are available both in the new areas of Catacombs and there are two in each old world dungeon. These are keyed to groups, but you can go in solo if you're good at taking on multiple mobs. For instance, a level 15 can go in solo to an AWID keyed for a group of four level 10s. Most of the mobs will be green and blue to a soloer, and maybe the "boss" will be yellow. Only the boss will drop items. Otherwise, the drops are aurulite and coin.
3) A few normal hunting areas, mostly for high levels, I believe. Not sure if they are soloable. Not sure on drops, except for aurulite.
4) Most of the new quests are of the "mini" variety and the reward is usually coin and experience only.
In general, a higher level character can probably do better pharming, and classes that have a difficult time with yellow mobs might find soloing the TIDs difficult and the AWIDs impossible.