Does regeneration occur infallibly, without exception, at baptism . . . particularly in the case of infants/children?
Regeneration is not infallible. But, as Luther says in his sermon, the baptism of children is more certain than that of adults:
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I think, if any baptism is certain, the baptism of children is most certain, because of the Word of Christ, where he commands to bring them, whereas the adults come of themselves. In adults there may be deception because of the reason that is manifest; but in children there can be no deception, because of their hidden reason in whom Christ works his blessing even as he has bidden them to be brought to himself. It is a glorious word and not to be treated lightly that he commands us to bring the children to him and rebukes those who forbid it.
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Does faith occur immediately consequent to regeneration?
Regeneration is the giving of faith and vice versa.
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But I wanted to know if you hold that any infant that is brought forward to be baptized must have at least one believing parent? Or... can anyone bring their child(ren) to be baptized?
1) I hold that justification is by grace through the faith of an individual. There is no such thing as a "proxy faith"; the faith of one cannot be applied to another.
2) My view says that if there is not at least one professing/believing parent, then baptism is not to be administered to their children. For, there is no "covenant baptism", i.e., the promise is to believers and their seed alone, should they be called of God and believe, and not to the world at large.
Luther, in the same sermon, says that ministers should not baptize recklessly.
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All this I say in order that one may not baptize recklessly, as they do who even administer it with the deliberate knowledge that it will be of no effect or benefit to the person receiving it. For therein the baptizers sin, because they knowingly use God's sacrament and Word in vain, or at least have the consciousness that it is neither intended nor able to effect anything; which is an altogether unworthy use of the sacrament and a temptation and blasphemy of God. For that is not administering the sacrament, but making a mockery of it. But if the person baptized denies and does not believe, you have done right anyhow, and have administered the true sacrament with the good consciousness that it ought to be beneficial.
Faith alone apprehends the promise of infant baptism. So, it would be reckless, indeed, to baptize a child brought by a parent who believes that baptism is just an ordinance to be obeyed or a mystical ceremony that saves by the outward act.
