[@Vec]: Well, to respond in order...

1. I didn't think that someone would take this route. Given the setting I have at the time (aka the Renaissance/Age of Exploration-era tech and stuff), there shouldn't be any need for these to even exist. If I was to list out every possible scenario that I wouldn't want being used, then I'd take over a month and STILL be missing things. It shouldn't be necessary to have to write out every single situation and what should and shouldn't be okay.

2. Malnourishment is malnourishment. Regardless of how much they are given, nobody with that much of a lack of a proper diet should even be able to scale an anchor or flee for extended periods of time, for example. If the captors are willing to treat someone like a guinea pig to the extent of kidnapping them off the streets, then there is a very clear disregard for human life here. Thus, they would likely only give the character in question the absolute bare minimum to live, else they would be wasting resources. It wouldn't make SENSE for them to use more than necessary. This isn't a charity case you're proposing.

3. [quote]When the ship returned a few months later[/quote]
I would think this to be rather intuitive. I shouldn't need to say that on oceanic voyage on a pre-industrial vessel would take a month or more; just because the engines we use today can be used to travel from one half of the Earth to the other does not mean that we have ALWAYS been able to travel at that speed.

4. Because it's not logical. You think it's going to be easy for people to retain knowledge that they cannot make constant use of and remember? A good memory is one thing, but tell me how often students will remember what they've learned in class after the summer.
Also, you're diverting attention away from the explanation behind the knowledge. Sanity and willpower? Okay, yeah, there are stories and I'll accept that much. But it's another to recall all that information from books after two years for the sake of doing so, especially when the character in question is attempting to work out an escape plan.

5. The problem here is that the character should not have been able to get to that position in the first place. Something like 'a stone that has something to do with amplifying lightning magic' is, as I assume it to be, a modified lightning catalyst. But simply implanting it in a person should have no lasting effects, and it is in essence just implanted for the sake of being implanted. It would eventually run out, and thus need to be recharged... Which means either removing it to recharge it (which is once again iffy because I would assume that given the prior statements this would be impossible without bodily harm) or exposing the character to electricity. Lots of it.
In which case, well... Then the problem becomes exposure to high-voltage electricity, but right now that's an aside. If it isn't, then it still becomes an issue because at no point have I said that such an object would even exist on the continent at that time.

6. As stated prior, malnourishment is malnourishment. Even if he isn't in peak condition, it's not exactly easy to flee from kidnappers, run all the way to a harbor, then dive off the side of a dock and scale the chains that hold the anchor onto the ship itself. Actually, I'm fairly certain that most children at that age would be unable to do all of that, even with a ton of adrenaline coursing through their veins. Remember, the chains will have to be long as the boat is tall and then some because of the depth of the water at the docks. The boat, given everything it is carrying, will have a height that would still be difficult to surmount.
So in the end, a 14-year-old child who is NOT in peak condition and has not had the chance to train their body freely is, in your form...
Able to run a long distance (minor pass because adrenaline);
Escape to a port town and outrun those who were supposed to guard him;
Dive into the water near the end of the night near one of the most highly-guarded vessels without incident;
Scale what is AT THE VERY LEAST an 80' long chain without incident in the midst of darkness while also having an electrically-charged jewel of some sort embedded within them (given dimensions of a ship from that era, this might still be underselling the height);
Have the energy required to climb on board, then successfully find an empty barrel and, without displacing anything that would make it seem suspicious, hide inside of it.

There's a limit to how far I'm willing to suspend my disbelief, but this is far too over-the-top for me. Still no dice.