As per my experience and this thread:
you can also use any weapons, magic, guardians and boom barels since they don't count as traps
So no, guardians do not count as traps. I believe barricades do not count either. If you're really ambitious, you might try for the no traps achievement at the same time, killing two birds with one stone.
Yes, there are different weapons in Orcs Must Die that you can unlock either via playing the story or from purchasing the DLCs.
Also, once you unlock the Elemental Weaver you can buy upgrades for your weapons during each map.
Same levels, as mentioned.
To expand on nightmare, the Orcs Must Die wiki page mentions that the changes in this difficulty are:
Decreased player health by 50%
Decreased rift points by 50%
Increased Mob health by 20%
Increased Mob damage by 20%
Orc Warriors have Shields
Guardians receive 20% less damage.
All breaks between waves (including at the start of ...
The blade-staff is the only weapon in Orcs Must Die that can appear radically different in its appearance as the model used for the weapon in-game is tied to the current character skin used. There are currently two choices the standard blade-staff can be switched to; The hammer which is available to customers who have pre-ordered Orcs Must Die and the double ...