If we stipulate the existence of Alice's language with the characteristics you describe, it's hard to see how it could be beyond any sort of analysis - but we'll examine that in more detail with Carol.
1. Yes. Alice being a native speaker of English, the court can demand that her testimony, if any, be in the same language as that of the proceedings.
2. Where she is a material witness testifying under oath with a grant of immunity, and there is reason to believe that the recorded speech is material to the proceedings - eg if she made a speech in her private language, and then remarked in English upon the subject of her speech.
3, 4 - likewise, insofar as she is capable. 2, 3, & 4 are all types of Funniest Joke in the World problems: if the communication is recorded in any form such that a person can understandably repeat it to Alice without themselves understanding the content, then the onus is on Alice to interpret the meaning for the court. (http://en.wikipedia.org/wiki/The_Funniest_Joke_in_the_World)
Carol, the human encryption engine
My understanding is that Carol also speaks English; that being the case, the same answers. Carol's lack of insight into her linguistic/cryptographic facility is irrelevant; after all, most people speak fluently in their native language without necessarily being able to analyze how. Illiterate people can't articulate rules of grammar but can still talk; likewise, one can toss a ball reliably without knowing the first thing about calculus or mechanics. This is a Chinese Room type of problem; unlike Searle, I don't think there needs to be an identifiable seat of consciousness. (http://en.wikipedia.org/wiki/Chinese_room) Like Hofstadter, courts are concerned with capacity and compliance, rather than epistomological understanding. It is enough that Carol be able to consistently exercise her talent on demand. There's a parallel to this situation with claims of facilitated communication for autistic or otherwise incommunicative people; some cases have fallen apart dramatically in court when the claims of interpretative ability were proved unreliable, though not before some defendants had their lives ruined with false accusations of abuse.
6. I'm unclear on what basis Ted was detained and his computer examined, and a defense attorney would certainly start by attempting to suppress such evidence if it was obtained via an illegal search. With a grant of immunity, one could compel from any of the three testimony about what contact had occurred between them, if any (eg whether Alice has ever met Ted or given anything to him), and likewise a good-faith attempt at 'translating' the PGP file - eg Carol might be able to decrypt it given a lucky guess at the key, if it were absurdly insecure.
7. If Ted is suspected and tried of possessing child porn based solely on the suggestive folder names, and a judge found no reason to suppress, then he would likely be acquitted since the naming of the folders was not done under oath. With no testimony on Ted's part, his defense counsel could argue that there are many possible reasons to engage in such activity. Perhaps Ted plans to create a fictional story about a child pornographer and intends to employ the laptop as a prop - the sort of prop that is often employed in movie and TV shows about police investigations. Perhaps Ted merely has a warped sense of humor. Perhaps he aims to entrap a child pornographer by connecting the laptop to the internet and seeing who downloads the files. Perhaps the files do contain video...of Ted's face as he imagines pornographic situations. The existence of so many possibilities casts a reasonable doubt on the supposition that the folder names are necessarily descriptive of their content.
But now take the file content as the hostile characterizations of the law enforcement personnel that you describe. This is potentially incriminating; not because it speaks ill of the legal establishment, but because we must ask how probable it is that the identity of everyone involved in Ted's legal case was foreseeable. If Ted lives in a small town with one cop, one sheriff, one prosecutor, one defense lawyer, one clerk of court, and one judge, and had some reasonable expectation of detention and search - eg a history of poor relations with the town's sole cop - then the involvement of these individuals with Ted's criminal prosecution was highly foreseeable, and it is quite plausible that Ted wrote his hostile prose as a description of what he expected to occur that day, which suspicions have been vindicated by events. In that case, the evidence would probably be exculpatory insofar as it demonstrated Ted's prior belief that he was going to be the victim of legal harassment, albeit in perverse fashion.
But since this episode takes place in San Francisco, a city of about 700,000 people, the chances that Ted could accurately predict the identity of everyone connected with his arrest and prosecution in advance are very low indeed. Ted would need to have either superhuman powers of foresight, or introduce additional evidence to show why that combination of individuals was rationally predictable - proof of corruption in the local legal establishment, or an enormously detailed knowledge of administrative scheduling and procedure in multiple different offices - police station, jail, DA's office, Sheriff's office, and Court. The probability of accurate foresight here is so low that a jury might infer Ted had encrypted multiple streams of information in advance and selected an appropriate key during trial: memorizing a list of all law enforcement personnel in advance, supplying a key representing the ordinal placement of the arresting officer Ted in an encrypted version that list, and using a decryption process that retrieved the name of the officer and substitutes it into a generic 'vile characterization' written and encrypted in advance. This would require a truly impressive memory for multiple long lists, but such feats of memory are not superhuman; there are professional entertainers who specialize in such feats and can explain or demonstrate them.
The probability that Ted had the time, capability and inclination to do this is demonstrably higher than the probability that he was clairvoyant or an incredibly good guesser. If, as seems possible, the specificity of the document rested on a trick of memorization and a selective decryption mechanism that could yield multiple valid-seeming plaintext values in response to multiple different keys, then a jury would have to weigh the possibility that the decryption process was intended to be obfuscatory rather than revelatory, and that there might well be a 'meta-key' that decrypted the files into video of child porn for Ted's illicit enjoyment. In other words, a perverse form of steganography that overtly identifies its significant content but frustrates its easy retrieval. Obviously this is all subject to the limits of information theory - if the size of the scurrilous prose plaintext file and the size of the encrypted files were both small and close - only a few kilobytes in length, say - then the probability that the encrypted files also contained contraband video would be correspondingly small. If the encrypted files were several gigabytes each, it would be entirely possible for them to include video, scurrilous plaintext, and multiple lists of names.
There would still, arguably, be a reasonable doubt about the nature of the still-hidden data in the file (if any), but the jury would be entitled to take these factors into account when assessing the defendant's credibility. On these facts, I think that Ted would have to be acquitted on charges of possessing child porn, as its existence could not be established beyond a reasonable doubt - if he were convicted, an Appeal court would probably free him. On the other hand, and subject to the estimable probabilities described above, I think he could be convicted of obstruction of justice for wilful frustration of the Court's fact-finding function - not by declining to comply, but by complying in such a manner as to strain the bounds of credibility.