Does analogueRead() change the way a number is represented etc?
There is no change in representation. analogRead() reads two I/O
registers, ADCL and ADCH, which on the Uno are memory-mapped to
addresses 0x0078 and 0x0079 respectively. It returns the result in a
register pair, r24 and r25, which per the AVR C calling
conventions is the
standard way of returning a 16-bit number. Thus, r24 holds the value
read from ADCL, and r25 the value read from ADCH. That's it. No
conversion whatsoever.

There is a change in interpretation... of sorts. The function is
declared as returning an int, which on the AVR is a 16-bit signed
integer, whereas it could be argued that the I/O registers contain an
unsigned number. However, since the sign bit will always be zero, the
signed/unsigned distinction is moot: either way the result will be
interpreted as a number between 0 and 1023.



Edit: As a clarification: the ADC register (which is another
name for the ADCL/ADCH register pair) is a 16-bit I/O register. At
the end of a conversion, it holds the 10-bit result right-adjusted into
this 16-bit space, zero-padded on the left, as follows:

-------- ADCH --------- --------- ADCL --------
0  0  0  0  0  0  r9 r8 r7 r6 r5 r4 r3 r2 r1 r0
----------------- ADC (16 bits) ---------------


where the bits r9..r0 represent the 10-bit conversion result. Since the
MSB is zero, it is irrelevant whether you interpret it as a sign bit or
as a regular unsigned bit.

Just for completeness, it could be noted that it is possible (though not
through the Arduino core library) to configure the ADC to left-adjust
the result, as follows:

-------- ADCH --------- --------- ADCL --------
r9 r8 r7 r6 r5 r4 r3 r2 r1 r0 0  0  0  0  0  0
----------------- ADC (16 bits) ---------------


In this case, the MSB could be one, at it would obviously be incorrect
to interpret it as a sign bit.

As a side note, the avr-libc defines ADC as
(*(volatile uint16_t *)(0x78)), which is unsigned. And it makes sense
considering that, unlike the users of Arduino core, the users of
avr-libc are supposed to know they have the choice to get a
left-adjusted result.