There are chests in every trainer platform, beside alchemy garden. You can find the key in alchemy garden if I remember correctly, and then look for the chest which fit it. You will get more keys by that to open up other chests.

You can use the teleport shrine in maxos chamber to teleport to the exterior of your battle tower and explore the sentinel island if you like to

You can re-skill your toon at your skill trainer.

There no armor or weapon vendors. Only sassan sells some potions and recipes, as well as raw materials. The morgue keeper also sell limbs part in necromancy ring. That the only 2 vendor you has in battle tower. Both dont carry too much gold either, but the morgue keeper should have more gold over sassan.