Free Trial Players cannot progress past Floor 10 in the Deep Dungeon during the Free Trial. So, experimenting with that is still limited. Additionally, as level is capped at 35, even if you did want to grind those 10 floors to get a feel for "end game" play, might still be restricted by that (although I do not know if that cap exists for PotD, but, between those two points, you probably won't get far regardless).

Free Trial Players also cannot use the market board, trade items, or use Mogletters, so no, as a free player, you probably won't be trading anything with anyone.

Since you cannot trade or buy off the market board, and are capped to level 35, you will not be able to unlock the glamour system (available to crafters at level 50).

Free Trial Players cannot join Free Companies (FF14 Guilds), so the only means of wider communication is to be invited to a Linkshell, which is a group of players typically with a specific theme to the chat. If what you're looking for is some sort of World Chat, this game does not have that feature.