Your character, inventory, containers, and skills all persist. If you die, you will find yourself spawning with your entire equipment and inventory wiped, but your character and any stored items will persist in the world. Merchants, traveling or otherwise, all have their active inventories that will reset based on the world clock; two days.
How it works
Your character, your skills and levels, your stored items, your property, your account horses, your written works, your saved animation sets, your bank balance and the names you have recorded for other people all persist across sessions. None of it depends on you logging out cleanly.
The exception is what is on your body. Equipment and inventory carried when you die are lost, and during the death timer they can be looted off your corpse by whoever reaches it first (see Death Has Weight). Gold in your purse goes with it. Gold in a bank account or a treasury does not.
Stored containers persist separately. A chest you own keeps what you put in it whether you are online or not, and who may open it is a question of keys rather than of who happens to be standing next to it (see Keys, Locks, and Locksmithing).
Merchant stock runs on the world clock like everything else. A merchant's gold and wares refresh on a two-day cycle, so what is on the counter today will not be there the day after tomorrow.
New characters are made in the launcher before you join the server, not from inside the world.
Commands (/help identity)
/character opens your character sheet. /sheet is an alias.
Your skills, levels and banked picks are read with /skill and /level (see Skills, Levels, and the Paycheck).