Welcome.
Melee Class - Traditional toe to toe bash the enemy is most likely gonna be a Sentinel class but you can also do successful melee in Rogue (Bladedancer), Primalist (Barb)and Mage (Spellblade).
Trading. There are LOTS of threads about this and I recommend reading the Dev Blogs for much more detail on this - Developer Blog - Last Epoch Forums and specifically Trade development update - Introducing merchants guild and circle of fortune factions
Dungeons. Yes, there are more planned but from what I understand this will be post 1.0 release. Dungeons are also the current way to bypass the campaign levels for advanced players. Monoliths are huge and there are both normal and empowered versions for end-game and loot hunting. Arena is niche content specifically for players that want never ending waves of enemies (not my cup of tea) - it was recently updated.
There is lots of more information provided in the dev blogs etc - far too much to repeat here and given the nature of the game , beta, there are lots of things that may change or be added to the game. E.g. lots of extra things for MP and trading are coming in the next smaller patches after 0.9.
The only real key part of the game that is still outstanding are the 3 remaining classes - which are confirmed as coming in 1.0.