so without spoiling but giving tips.
for eikthyr's trophy. go to the original world spawn and hang it on the hook on the stone with the deer pic.
if you're fighting trolls you're on the right track. keep exploring.
grab everything! you'll unlock recipes by picking it up its ingredients, so pick up everything. as recipes unlock check your workbenches and hammer for those new things you can make, and then make them.
yes there are bigger chests and more building options.
organization is your friend. i typically keep a few chests near my benches, rather than having a warehouse. tip: you can use the 1x1 floor as a sort of shelf to stack your chests.