I can make your list even simpler but include one of the major criteria to be a Muslim, which perhaps you forgot to mention.
1)Faith in unity of God and firm belief that Mohammad Mustafa PBUH is the prophet of Allah.
2)Offering five time prayers a day
3)Fasting
4)Zakat
5)Haj (for people who can afford)
Person who obeys above five pillars of Islam with clear heart is a Muslim. Though every pillar require more explanations particularly faith in Unity of God and belief in the last Prophet PBUH.