Can a simulacrum use magic items such as wands? Would it matter if the item requires Attunement?
Yes, it can use items
The only differences between the simulacrum (Player's Handbook 5th ed, p276) and the target creature are that it has half as many hit points as the original, it is formed without equipment, and that the simulacrum cannot gain abilities, advance, or regain expended spell slots.
The duplicate is a creature...and it can and take actions and otherwise be affected as a normal creature...
...Otherwise, the illusion uses all the statistics of the duplicated creature.
It can use items provided to it, and attune with them as normal.
@keithcurtis noted that since items can only be attuned to one creature at a time (Dungeon Master's Guide 5th ed., p 138), the simulacrum is not attuned to the items that the target was at the time of the simulacrum's creation, and must attune as normal during short rests.