Its not enough to have lod installed, you should also have your character to be "expansion" one, noted in the character list. Try to create a new character. If you see "expansion" checkbox in the creation screen, everything is fine. Probably there is a way to convert existing single player char to exp too.
yups click the original (classic) character and pick convert to expansion (on the bottom of the screen).
For your other question: Wielding a 2h will automaticly let you use both weapon slots. (wielding a 1handed weapon opens up a slot for a shield). Only Barbarians are able to wield 2h swords at the same time. And both assasins and barbarians can wield dual 1h weapons (assasins only dual claws)
The second weapon slot only appears if the character is expansion. If you convert the character to expansion. The character will have a stash that is almost as big as half the screen and you can press the weapon switch button, 'w' by default, to have it switch between two different sets of weapons.