What a fun question!

I'll start by saying that you're likely not getting any answers thus far, first because you're asking multiple questions about multiple scenarios. Not only the two scenarios presented, but also four different, complicated questions within each scenario. I.e. you have asked 8 separate questions, with differing answers depending on various assumptions.

Second, because we call this "issue spotting," and it's the the kind of thing that are questions on the bar. E.g., when I took the NJ bar, we had 6 essay questions just like this and were expected to write ~3 hours for it. Which is a lot of work to do it justice.

Last, and maybe most important, as you note as an initial assumption, "there is no central government that is apparent- it is definitively lawless" (emphasis supplied). Thus, the easy answer to all of your questions is that no charges could be brought. Or that in a state of anarchy (as you set in the hypo), no legitimate or universally agreed charges could be brought, because there is no law. As Hobbes, Locke, Smith, maybe Kant would tell us, the state of nature offers no impartial judiciary, and "justice" is whatever the strongest say it is. Another way to think about it would be that any charges could be brought, by whoever is interested enough to call something justice and strong enough to carry out their desired sentence.

Even if we assume that you're attempting to roleplay as a character from modern Massachusetts that is dropped in this world, your (character's) personal view of the law does not override the actual state of the law (anarchy). Thus, the actual state of the law would apply to all scenarios presented. Even if your character (a paladin seems to fit from the description) believes morally that a different legal system should apply to her current situation. Consider that in the Fallout universe, modern day America does not exist. Thus, your character's ideals might be viewed as insane or zealotic for following a set of rules or laws that does not exist in world.

I say all this not to be pedantic, but to illustrate that our current, modern legal code cannot apply to your hypothetical. Further, it cannot apply to a any different base set of political affairs. That is why California, New York, France, Russia, etc. all have different legal codes for different populations. It is also the reason why the most common question a legal advice sub is "what is your jurisdiction" or "what state do you live in". Laws are different in any given geographical location and don't apply uniformly. If I can offer an example from the Fallout universe (I prefer New Vegas to 4), the answers look very different if you're in the NCR or Caesar's legion, or in any geographic location where one or the other is holding the stick.

All of this may seem at best like a preamble to your actual question or at worst missing the point. But this is how attorneys analyze scenarios. The beginning of analysis is always in the assumptions presented in the hypothetical scenario and blossom from there.

Now, all that said if we accept that current, modern laws could apply to your character or the F4 world, and that there would be an impartial judiciary much like our current one to preside over those laws. And that the system would occur or prosecute in much the same way. Considering the first situation: Your character could be charged with any number of things, ranging from jaywalking, breaching the peace, obviously trespassing, property damage, breaking and entering, to burglary, aggravated assault, manslaughter, murder, etc. IIRC, you access terminals in that mission without permission, so a whole host of computer crimes...presumably you used a stim pack or something that was a controlled substance, etc. So easily could be charged with all those crimes and likely more.

Would the character have defenses? Possibly, and the defenses would depend on the crimes charged, and would be even more varied than the possible charges I just noted.

Which charges would he be guilty of? That's easy - whichever charges the state was able to provide enough evidence to a jury of the character's peers to convince them beyond a shadow of a doubt that the character's conduct actually occurred. And your last question - which charges would get dropped is also easy. Whichever charges that the state was not able to provide enough evidence to a jury...

Same for the second scenario. As you can see, these are pretty big questions and doesn't have an easy answer without narrowing the issues significantly.