1.. My understanding is that electrical outlet, 13A sockets, must be
at least 300mm from a sink. Is this correct?

It's more of a guideline than a rule.

4.. We are fitting a built under double oven and ceramic halogen hob. My
question here is how to wire this in. The Oven is rated at 5.18 kW (22A @
230V) and the hob at 5.4kW (23A @ 230V). Currently the MCB for the slot
in
cooker is 32A. I will upgrade this to 45A. My idea is to run 10mm cable
from
the MCB to the Cooker switch above the counter top, and then run two 6mm
cables from the cooker switch to cooker outlet plates below the counter
top.
Is this OK?

32A would be fine. There is no need to upgrade to 45A. I would keep the 32A
for increased short circuit protection, particularly if the cable runs are
long.

You may have difficulty getting two lots of 6mm cable into the 45A DP
switch. If so, you can probably use 4mm cable for the runs to the cable
outlets. Although 4mm can't take the full 45A, I believe you are permitted
to take advantage of the fact that a heating device is unlikely to produce
an overload situation beyond the total sum of its heating elements as there
are no failure modes for a heating element to do this. 4mm (even 2.5mm)
cable is quite capable of carrying the 23A that each appliance needs.

This assumes that the runs between the DP switch and cooker outlets are
short (they should be, as the outlets must be close to the switch). If not,
you may have trouble using the MCB for short circuit and earth fault
protection, as the earth loop impedence may be too high.

Christian.