Q1
Not a good idea to think of the carrier as something to "reduce the wavelength"
It is better (in my opinion) to think of the carrier as the thing which carries the information.
The frequency used will depend on where and how far we want to send the information.
The frequency determines the wavelength and hence the physical size of antenna we require.
Audio frequency, yes within the equipment we are always thinking about an electrical AC signal at audio frequencies. Not sound vibrations in the air.
Q2
Yuk!
A Channel is a given frequency with spectrum space on both sides to allow for the modulation.
Example, VHF Marine Band as used by ships.
Channel 0 156.000Mhz
Channel 12 156.600MHz
Channel 14 156.700Mhz
Channel 16 156.800Mhz
When originally specified, the channels were spaced at 50khz intervals (note: this is no longer true, but lets keep it simple)
The channel spacing allowed room for the FM modulation so that adjacent channels did not interfere with each other.
Your example of telephone system is poor, particularly with more modern practice.
In a real FDM telephone system, each voice signal would be modulated onto a carrier, so we would have several carriers grouped together and in turn modulated onto a higher frequency carrier to send down the coax line or the radio link.
(I think that I just made this description worse!)
Q3 The basic antenna is a half wave dipole.
It is a half wavelength long at it operating frequency and is fed in the middle.
(There are also monopole antennas which need to work over a ground plane, but in the interests of simplicity I am ignoring them).
An antenna which is much shorter than a half wave will not work very well.
An antenna which is much longer than a halfwave will work ok, but its characeristics will be different from the halfwave dipole.
Q4
The pictures you have of a VHF and a UHF antenna, are only defined a VHF or UHF because of their physical size.
Make the VHF antenna smaller and it is a UHF antenna.
Make the UHF antenna larger and it is a VHF antenna.
Polarisation.
If the elements of the antenna are horizontal, it is said to be horizontally polarised.
Similarly, if the elements of the antenna are vertical, it is said to be vertically polarised.
The antennas at both ends of a link should be of the same polarisation, otherwise there will be a BIG loss of signal (in practice, about 20 or 30dB).
The same it true for whip antennas!
The whip antenna on a broadcast radio litening to a local station has so much signal that the loss due to incorrect polarisaion is not usually noticed.
JimB