The first question will be addressed in this posting. Kant speaks of a constitution that is republican as including principles that operate on three distinct levels. At the level of individuals there is a principle of the freedom of members of a society whilst at the level of subjects there is one of dependence on a single common legislation. The third level is that of citizens of a state where there is a principle of equality operative. Kant's general claim is that the "idea of the original contract" leads us to the notion of a republican constitution.
In articulating further the notion of this constitution Kant develops his argument in another extended footnote. The footnote begins by opposing a conventional "liberal" idea of freedom as "the warrant to do whatever one wants provided one does no wrong to anyone". This view of freedom is what Isaiah Berlin characterized as "negative freedom" and is captured well in John Stuart Mill's definition of freedom as "pursuing our own good in our own way, so long as we do not attempt to deprive others of theirs" (On Liberty). Kant indicates however that this view amounts to an empty tautology.
By contrast to this view Kant defines freedom as "the warrant to obey no other external laws than those to which I could have given my consent" (Ak. 8: 350n). The reference here to hypothetical consent was not included in the "negative", "liberal" view of freedom and nor was the specific inclusion of external laws. The specific inclusion of the concept of law in the idea of freedom is subsequently followed up by the ways in which Kant characterizes equality. Equality within a state is "that relation of its citizens in which no one can rightfully bind another to something without also being subject to a law by which he in turn can be bound in the same way by the other" (Ak. 8: 350n). So the equality in question is one of reciprocal relation to the laws of the state. Kant intimates that there is no need to further specify the dependence of subjects since we have already covered it in what has emerged.
On the grounds of the egalitarian conception of citizenship Kant explicitly rules out the notion of hereditary nobility. The republican position advanced is one in which freedom is distinctively understood as emergent from a relation to law, not as something properly realized independently of law. This is the substantive difference between the republican view that Kant has advanced here and many "liberal" views. It remains to be assessed, however, what relation this puts a specifically Kantian theory in to the so-called "Kantian liberals", such as John Rawls and his followers on the one hand, or the more apparently "republican" views of Jurgen Habermas. A further point of interest is how to characterize Kant's form of republicanism by contrast to that which has been developed in contemporary political theory on the basis of response to the Renaissance account of Machiavelli. For a detailed description of this tradition and its place in contemporary political theory see this article. A notable feature of the contemporary revival of republicanism and assertion of its distinction from liberalism has been the general failure, despite the historiographical nature of its basis, to account for Kant.