...why does Eve/Darklaw wanted to jail Ms. Cantabella in London? Remember that she made a deal with the prosecution to declare her "guilty"

My guess would be she brokered a deal for a fine and probation or something - stuff that could be easily swept under the rug by Arthur's company. I don't think she was actually trying to send Espella to prison.

Is Arthur's company not what they call Labrealum in the localized version? aka. the company the Storyteller works with?

If I recall correctly... Darklaw was the Great Witch, right?

It is evidenced by how she freely casted magic in London and in Sir Belduke's residence without using the scepter.

How come that she was able to say "Granwyrm" during the trial, without activating it?

Because "magic" is the work of Shades like stage ninjas during movie/theater productions. Since she's in charge of them all, why would she summon a giant fire dragon and essentially convict herself?

Besides, "Bezella" and the "Great Witch" are two different things.

Ah, right. I just figured they did that whenever someone who was supposed to be a witch said the incantation. Yes, I guess that makes sense.

So in the end, we learn that magic doesn't exist, right? Then how does the intro make sense, what with the statues coming alive and attacking Carmine Accidenti and Espella? At first I thought it was that they were still under the influence of the hypnosis gas and whatevers and imagined all that, but that doesn't explain how that handprint ended up on the car. I mean, Layton mentions it, right? That there is a weird handprint-dent in the side of Carmine's car and that it's too big to be a normal person's but is the right size and shape for the right hand of a statue near Carmine's crash site, even though the statue is holding something in its right hand? Frankly I don't think that Eve would be so rash as to actually bring shades out of Labyrinthia and create 'magic' outside of it, in London and all, especially since 'Labyrinthia' was top-secret.

machines

It is explained in the Special Episodes (which are pretty much development commentary made by characters) that part of the park was bought by Labrelum Inc.

In short, the moving statues are robots. Probably the part with buying public ares is also how they got the secret passage thing installed at the bridge.

The same tech is used in London. Since the magic doesn't actually start until Layton and Luke have been affected by the ink gas, for all we know, Darklaw and her gang could have been hiding jetpacks, turbo fans, and flamethrowers somewhere, and they'd all be paid for by Labrelum Inc.

So I get that "magic" wasn't actually real, but then how did the fire dragon appear? We clearly see it flying around.

That was just the imagination of a confused, despairing child. Espella just thought it would fly around. See?

In one Scene Maya and Phoenix just "disappear" and then they are in the book. How does it work?
And: How did the huge gate disappear?

That was a visual interpretation, of course. In reality they were probably given a glass of water earlier in the lobby and knocked out by the silver bells.

Bringing them by accident was a complete lie on Darklaw's part. Bringing someone requires way too many preparations (and dragging people from a goddamn courthouse) to be accidental. She was probably unwilling to actually give Nick any credit. Where did I hear that before...?

My best guess is that she had a little bit of trouble with Phoenix knowing about Espella and seeing her in such a condition, I believe.

No no, not that dragon. The dragon that appears in front of everyone, "killing" the Storyteller. The dragon Espella saw was explained, but not the one that everyone in the entire town square saw.

She does get incinerated though.