The Ki Serenity Necklace increases your Ki Pool by +2 (4 levels) and your effective level for Ki Ability by +4. Would a Qinggong Monks spell like abilities count as KI Abilities for the purpose of this bonus given they use Ki?
No, the Necklace of Ki Serenity would have no effect on your Qinggong Monk abilities, except to give you more ki. When it says it increases the "level-based effects of his ki pool ability", it means the ki strike abilities.
For example, at 10th level your unarmed attacks are treated as lawful weapons for the purpose of overcoming damage reduction; with the necklace on, you'd get this ability at 6th level instead. That's all.