Curiouser and Curiouser

Question

CHAPTER ONE

Alice was beginning to get very tired of sitting by her sister on the bank, and of having nothing to do: when she was overcome with the strangest sense of deja vu, and saw a 7x3 grid of letters in her mind's eye.

'Why', she declared, 'I can spell out my name, ALICE, moving orthogonally from cell to cell!' Orthogonally was an exceptionally long word, and Alice felt quite pleased for having used it.
'I could also spell out MARCH, HARE, WHITE, HEARTS, and CHESHIRE in the same way!'

Alice tried to focus on the 7x3 grid, but could only remember a few letters:

Alice, thinking herself very clever, managed to recreate the grid of letters. 'That was a fun adventure,' she muses, 'but whatever am I supposed to do now?'

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CHAPTER TWO

All of a sudden, the Red Queen appeared, and broke the grid into pentominoes, leaving behind a single square.

'Yes, yes,' she tittered to the knave accompanying her, 'these pieces are fabulous. The letters on each piece can be rearranged to spell out a common 5 letter word... well, one actually spells out a 5 letter male name, and this name does ring the strangest of bells. I wonder where I have heard of him. Let us away!'

The Red Queen and her knave began trotting off, and Alice felt very angry that they had taken apart her grid of letters! Pocketing the letter they left behind, Alice began to run after the Red Queen and her knave.

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CHAPTER THREE

Alice finally caught up with the Red Queen, rather out of breath. The Knave had built the Red Queen a new palace out of the pieces, a majestic 6x4 building, without even flipping any of them! Alice couldn't help but notice that the 4 pentominoes the Red Queen stole were not enough to build the house; the knave had also procured a piece called 'ROOF', which was positioned like so:

'Excuse me,' Alice yelled, 'but those are MY letters! I would be ever so grateful if you could give them back!'

The Red Queen shouted back, 'Nonsense', and before Alice could work out what on earth was going on, she found herself in the middle of a dark hedge maze.

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CHAPTER FOUR

Alice was beginning to feel very lost and hopeless, when she came across a blue caterpillar smoking a pipe.
'Excuse me, good sir, but do you know the way out of this maze?'
The caterpillar handed a map to Alice, not once taking the pipe out of his mouth.

'This makes no sense!' Alice proclaimed.
With a sigh, the caterpillar stopped smoking. 'You are here.' He pointed at the circle. 'You want to get here.' He pointed to the line leading away.
'But what are all these numbers?'
The caterpillar grumbled. 'On top of each hedge (each white square) is a jubjub bird. Now some of these jubjub birds are angry, and are on the lookout for prey (the arrows tell you which directions the angry ones are looking). If a jubjub bird does not see you pass through paths in the directions they are looking EXACTLY the number of times specified, they will gobble you up before you can leave the maze!'
'So, to make sure I understand, I can't pass through the path right above the jubjub bird marked zero? And I will pass through seven paths in the same row or column as the jubjub bird marked seven?'
'Sounds good... just don't reach the same intersection more than once...' He put the pipe back into his mouth, and Alice knew it was up to her to get out now.

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CHAPTER FIVE

Upon exiting the hedge maze, Alice found herself by the river once again, her boring sister still engrossed in a rather uninteresting book.
'How curious', thought Alice, 'That my adventure has led me back to this bank... hold on, what's this?' Alice picked up a book floating in the river.

THE JUBJUB BIRD
The jubjub bird is a curious thing
Jubjubs are not pretty, nor can they sing
They shan't fly over the path of a girl
Who has come from another world.

Jubjubs that fly far east tonight,
Are out of mind and out of sight.
The 8 jubjubs that can't fly far east,
Are quite important at the very least!

These important places each
Will take a letter from the Red Queen
Remove (just one of) what you have pocketed away
And rearrange to find the most curious name.

Curioser and curioser, thought Alice, as she wondered about the poem. As her sister called her to come home, Alice solved the riddle and found the most curious name.

'Golly gosh!' She cried in alarm.

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WHAT IS THE MOST CURIOUS NAME? WHY WAS ALICE ALARMED BY IT?

Answer 1

Partial answer:

Chapter 1:
Solved by Volatility

Chapter 2:

Chapter 3:

The words anagramed here are:

Lewis (Rather well kown for this theme)
Their
Match
Reach
Roof (the one already in the grid)

Which means Alice is left over with the extra

E

Chapter 4:
Solved by Deusovi

Chapter 5:
With a bit of Deusovi's help for pointing out that:

The areas that don't have an exit East total 8 letters
Those letters are SEEHACLR.
Removing my pocketed "E" and anagraming what left gives
Charles

This may be alarming because it's:

her father's name or perhaps because it's Lewis Carroll's real name

Answer 2

Partial answer

Chapter One grid

After the edit, this grid satisfies the constraints:

M C H E W L I
A R T S H A C
E H E T I R E

I don't know whether this is the only solution or not, but this was my general thought process:

Assuming that there aren't any extraneous letters, MARCH must start in the top-left corner, since it is the only word with an M in it.
If we then assume that there is only one S in the grid, then both HEARTS and CHESHIRE must pass through the centre square. Noticing that both these words share a bigram with MARCH (AR and CH respectively), we can fit letters in the grid assuming that these bigrams are indeed shared letters in the grid paths, leading to the left part of the grid being
M C H E . . .
A R T S . . .
E H . . . . E
Then, noticing that the latter half of CHESHIRE differs from HARE by only one letter, and assuming the H and RE are shared between them, and keeping in mind the remaining words, the grid fills itself in.

Chapter Two words

A possibility for the words are:

CHARM, TEETH, REACH, and LEWIS, leaving the I on the bottom row left out. Now where might I have heard that name before?

Here's a visual:

However this partitioning doesn't work for Chapter Three...

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Sidenote: Chapter One in its previous form could be solved using only 19 letters, in the following way:

M A E H W . .
C R T I R E C
H E S H A L I
(additionally, the ALICE could start in the top-right corner and go clockwise for an alternative 20-letter solution)

Answer 3

Partial Answer: Chapter 4 Maze

The first thing to notice is that the start and end are in the same column. This means that every column must be passed through an even number of times. Similarly, every row must be passed through an odd number of times.

Look at the two 1s pointing at each other. If there is a line in between them, then there are no other lines in the column, and you cannot return once entering the left side. This means that there must be no lines between them, so there is one under both 1s. Similar logic with the 3s leads to this:

Now look at the 2s in the top row. There must be two lines to the right of the 2>, and two lines to the left of the 2<. They overlap in the middle: however, since we already have a line in that column (by extending the top left), the "overlap" in what they see must be only one line. This means the far right of that row must have a line in it to satisfy the 2>.

Combining this information with the 0^ clue gives us:

Now we know where the overlap is: just left of the 0^. We can fill in that line, then blank out the rest of the lines in that row.

Consider the row with the far left 2>. We know the 2> must see two lines - an even number. But as we said at the beginning, it must go through that row an odd number of times. This means that the line to the left of the 2> should be shaded.

Now look at the row with the 5^v<>. You can't go through all three of the columns in the left section, and you can't go through three columns in the odd section. This means at least 3 of the 5's visible lines must come from the column, since the row can't provide enough. (And of course, it can't be 3 since 3 isn't an even number and all columns must be passed through an even number of times.)

This means we can fill in the remaining lines in the 5's column. Cleaning up some satisfied clues and impossible lines gives us this:

Now keep looking at the 5. It has four of its lines taken up, and one of the two lines to its right must be traversed. That lets us cross out the whole row on the right section.

More parity on the 5>^< lets us fill in the line above it. This means that there must be 3 lines in that row traversed, letting us fill in the two lines under the 5<v>. After that, some trivial deductions lead us here:

And now we look at the 3< on the bottom row. At least one of the bars it sees must be in the right section (to get back down from the top of the 5<^>), but that means both must be (because there can't be only one bar on the left). That lets us complete the bottom right area.

And finally, we look at the 7^v<>. There are two possible paths to take (since the 3< is satisfied), and only one satisfies the 7. This gives us our final path of:

--er, I mean...

Answer 4

EDIT: The issue pointed out in this post has been fixed.

I believe Chaper 1 is underconstrained; I've found several (arguably 'better') solutions in addition to the one posted by Volatility above. I see in the comments that one was the intended one, but here is another set:

M A R C H L A
H E T S E I C
A R I H W ? E

ALICE on the right can be rearranged in a number of ways, as it
doesn't have to cross anything. If you interpret the puzzle as
saying all squares must be accounted for, you can just have

M A R C H I L
H E T S E C A
A R I H W E E

, with the given square in the bottom right not used in any word.

It seems very likely that it's impossible to proceed if you find this solution first, which is unfortunate, so I hope it's easy to fix! I'm going to take Volatility's solution and go on to Chapter 2...