First off let me say that Kevin, Kendall and Sophia are absolutely correct in their reasoning why most people have not responded to you B is B. That being said I am responding to these questions because I like to think of how Objectivisim applies to the world.
I am not interested in exchanging point and counterpoint of view with you because frankly I don’t care what your point of view is. Up to this point I see no indication that you are not a Troll, so I’m doing this for my pleasure, not for your enlightenment, even if you made such a thing possible by engaging in honest debate.
Q1: What would be the legal system’s stance or repeat felony offenders?
Logically a chronic offender would be identified as such. I’m not a lawyer but I’m sure that there is some accepted rational way of determining dangerous recidivism and applying the law to solve the problem.
Q2: Would there be an age of legal consent for sexual relations, and if so–what would be that age?
This is a good question and one that I’ve not worked out to my own satisfaction. I want to say that the age would depend on the maturity of the individual but I also see the need to protect the young from perverts and predatory monsters. I don’t have the answer to this.
Q3: If all property within the Objectivist nation was private, what would happen if I decided to let a foreign military set up an intelligence gathering facility on my property? (For which I charge them money of course.)
That action would be in direct opposition to the continued security of the Objectivist nation and fall under the scope of Governments mandate to protect the nation. Therefore you would not be permitted to do it.
If you are getting at the idea that it is your private property and therefore it is yours to do with as you wish you are confused. Just because you own a piece of land that ownership does not make it your tiny little fiefdom where you get to decide what laws apply and what ones don’t. You can’t commit murder and claim the right of property protects you from the consequences because you did it in your bedroom.
Q4: Would the Objectivist nation have its own intelligence gathering apparatus–would that fall under the role of military? Would they have a foreign intelligence unit similar to the CIA, and if so, what would be their charter of operation and use?
In my opinion the answer to both of these questions is yes.
The domestic “intelligence gathering apparatus” would be a police asset and would possess the ability to delve more deeply into criminal activity and organizations that the regular police could, kind of like an SIU on steroids. This entity would not be controlled by the government but by the police. It could be called on by government but there would be a need for the police to have probable cause for the entity to investigate.
Of course there would be a foreign intelligence asset. It would be in the interest of our nation to know what nations hostile to us are doing.
I‘m not going to go into charter and use issues… I don’t have time to write a book on the subject. 
Q5: Ayn Rand stated that “rogue” states that didn’t value the rights of its citizens were freely open to attack. Who would be the determining body in a legal sense for this type of action?
For a start I’d say the government with the support of legal authorities. A referendum might be a possibility though I’m unsure.
Q6: Could you apply the same philosophical justification that Rand does towards rogue states to individuals within the society? Thus, if an individual fails to respect the individual rights of other citizens are they open to violent physical attack by any citizen? What would be the legal framework for these types of actions?
No. States are instituted by people to protect their rights. Once this is done the state owns the right of the retaliatory use of force, individuals (except in emergency cases) do not. If the person was assaulting you then you have the right to fight back. If he cheated you in a business deal you would have to go to court. You could not take him out into a back alley and blow his brains out.
Q7: In an Objectivist society who takes the responsibility for building and maintaining the roads, bridges and freeways? If not the government, how would a private enterprise be able to charge for roadway usage in a manner that doesn’t involve a toll booth every other block? Are the sewer systems also to be privatized?
As far as roads go I have already stated my ideas on this subject here
I would think the sewer system could be. To be honest I hadn’t thought about that piece of infrastructure yet. Just off the top of my head…
I would imagine that there would be more septic systems in use. It also isn’t practical for there to be more than one sewer company operating in a particular area, say a subdivision or larger, city even. That company would in effect own a monopoly on those services in that area. But the individual residents would still be able to choose between that or a septic system because a city would not be able to tell them they couldn’t have a septic system installed (as most can today).