If I play King's Edict, can my opponent play Not So Fast and counter the spell?

No, your opponent cannot use Not So Fast to counter King's Edict.

According to the card text and established rulings:

1. King's Edict does not target: As confirmed by FAQ #509, King's Edict does not choose or target any units when it is played. Instead, it instructs players to make choices during its resolution.
2. Not So Fast requirements: The ability on Not So Fast specifically states it can only counter a spell or ability that "chooses a friendly unit or gear." Because King's Edict does not choose or target anything, it does not meet the requirement for being a legal target for Not So Fast.

Summary of the interaction:

• You play King's Edict.
• It is placed on the chain.
• Your opponent attempts to play Not So Fast targeting King's Edict.
• Because King's Edict does not choose a unit or gear, Not So Fast cannot be played to counter it.

This is consistent with the logic found in FAQ #8446 and FAQ #8559, which clarify that Not So Fast is restricted to countering spells or abilities that specifically choose or target friendly units or gear.