Thank you for appreciating what I posted. Anyhow, I think it is important to correct something you wrote.
Your concept is right, that first group of people one should give zakat are those Mustahaqs who are closely related, followed by neighbours, other relatives and those around you. Then only people in other categories come. In all cases, religion does not matter.
Anyhow, important thing I want to mention here is that, a person cannot give Zakat to own parents or own children. Further, Husband cannot give Zakat to his wife … though wife can give zakat to her (mustahaq) husband.
Why? … Because, those who are responsibilities, one cannot give them Zakat. Needs and responsibility of parents are on children, hence children cannot give them Zakat. Same is the case with children, as they are responsibility, one cannot give them Zakat.
[Well, according to Islam, children are fruits and parents are tree, thus whatever is there of children belongs to parents, just like whatever is there of fruits belongs to tree. Thus, children cannot give zakat to parents, as whatever children own belongs to parents anyhow].
As for wife/wives, since they are responsibility of husband, it is their right to get what they need, thus husband cannot give zakat to wife/wives.
Since husband is not financial responsibility of wife/wives, she can give zakat to husband if husband is mustahaq (eligible to receive Zakat).
Thus, when we talk about relatives, we talk about uncles/aunts, siblings, cousins, etc. If they are mustahaq, their right to receive Zakat is more than others.