There's a lot of different things going on in your question(s).
I'll start with the last one:
according to Kant, every citizen in a state should, theoretically consent to the law, even if not in practice.
While there's a type of consent at work here, there's something more important involved in Kant's understanding of citizenship in this moral kingdom (or realm if you prefer). Viz., each citizen is rational and therefore arrives at the conclusions of reason as to what sort of laws would be harmonious for the kingdom to work. Thus, it becomes a kingdom of ends.
In other words, it's not that there is ever a moment that asks for our consent based on personal preference, taste, or advantage. Rather, the consent is that as rational beings we consent to rational laws.
This is there in abbreviated form in the Groundwork but an extended treatment of the relationship of the members of this community is handled in Religion within the Bounds of Reason Alone
Your other question seems to focus on how Kant handles laws. Fortunately for us, Kant wrote a book about that called Rechtlehre translated either as Doctrine of Right or Metaphysical Principles of Right. This constitutes the first half of Kant's Metaphysics of Morals (not to be confused with the Groundwork of the Metaphysics of Morals).
In that text, the basic flow of how laws and rights work is that they proscribe those actions Kant believes are necessarily immoral. In other words, Kant thinks that we can as a society proscribe lying, murder, cheating, adultery (and any sex outside of a heterosexual marriage for that matter), and many other things. For each of these, Kant's arguments (which range a bit in quality) relate back to the idea that such actions are not capable of having a moral motivation, i.e., they could not be universalized OR they are not compatible with acknowledging rational persons (which Kant calls "humanity") as ends.
Thus, the test of any law is not whether it is law but whether it is a law that requires us to make exceptions for ourselves or others. OR for Kant, what is synonymous, whether it treats humanity in ourselves or other persons (even non-human rational persons) as mere means to our ends rather than as rational ends in themselves.
So Kant most definitely believes a law can be unjust. Specifically, any law that say would make it so that one person can use another (slavery) or any law that enables people to cheat others or that enables lying to prevail or dismantles private property.
Thus returning to your bullet points, the "equality" in the Kantian system is always founded on the fact that each of us is a rational being. In this respect, it differs from a social contract theory that is compatible with the three bullet points you identify.
Again, the same qualifier must be added to "freedom." Kant believes we are empirically determined creatures but simultaneously that we possess rational freedom to determine our actions (per the third antinomy in the Critique of Pure Reason and elsewhere).
"Independence" too must be understood not as freedom to do whatever but as the ability to do what reason demands regardless of the actions of others or our passions.
I'm not sure if the above addresses what you intended to ask or not, but I'm having a little trouble finding the question.