The Citizens Advice question has been answered above, so this is about the second one.
Two things a 17-year-old interested in law and social justice can do that cost nothing and don't depend on anyone accepting an application.
Sit in the public gallery of the local magistrates' court. Hearings in England and Wales are open to the public and there is no booking; he turns up, goes through security and asks the usher which courtroom has a list running. A morning of first appearances and pleas gives a truer picture of what "the law" actually is than any book, and most of it is housing, driving offences, benefits and people who have run out of other options, which is exactly the social justice end of things. Worth ringing the court first only to ask which days are busiest. Crown Court is open too, but the magistrates' court is closer to the kind of problem Citizens Advice deals with.
The reading version is The Secret Barrister, and Just Mercy by Bryan Stevenson if he wants the American side of the argument. Both are very readable at 17 and both give him something concrete to say in a personal statement or an interview. "I went and watched" always beats "I am passionate about".
Two structured programmes are worth checking now, because the deadlines tend to fall early in Year 12. The Sutton Trust's Pathways to Law is free, runs across both sixth-form years and includes a short placement with a law firm or chambers (there are widening-participation criteria, so check whether he qualifies). The Bar Mock Trial Competition run by Young Citizens is entered by school teams of 15 to 18 year olds, so worth asking his sixth form whether they field a team and, if not, whether they would. Many sixth forms also have an Amnesty group; if his doesn't, starting one is itself something to write about later.
On the EPQ, the usual trap is picking a topic ("social justice") rather than a question. A question that joins his history A-level to the law interest will be easier to research and much easier to talk about afterwards. How a specific piece of legislation was fought for, or why a particular miscarriage of justice took as long as it did to overturn. Narrow beats grand every time.
On what a week of admin and shadowing actually teaches, since you asked. Less than an advice role, but not nothing. He would see how an advice interview is structured, how much of "helping people" is chasing a form or waiting on a phone line, what confidentiality looks like in practice rather than on a poster, and, probably the most useful thing, whether the reality of the work appeals to him or only the idea of it. That last one is worth a week on its own, whichever way it comes out.
On the confidence point, something with a fixed shift, a clear task and a definite end usually does more for a wobbly 17-year-old than a prestigious placement that asks a lot of him. Food banks (most take volunteers from 16) and parkrun both take people his age and neither will ask him to be anything more than reliable. Confidence tends to come back through doing small things well and being thanked for them, not from finding the perfect thing.