So Q1: Can I just parallel up the heat sources like this, and just tap
into the top and bottom of the tank round its periphery with 3 inlet &
outlet pipes to the various heat generators? Each one will be pumped
(Although the cooker right now is gravity fed)

It won't be expensive. A suitable exchanger costs around 80 quid. The cooker
can (and probably should) stay on gravity circulation if the heat bank is
sufficiently above it with wide enough pipes. Having reliable gravity
circulation is better for the health of your average cooker back boiler,
especially if solid fuel.

The controls for this system are relatively simple. You shouldn't need any
external control boxes. It only gets a little complicated when it needs to
make decisions like "should I run the gas boiler, if I'm already getting
solar heat". Even this can be simplified by having the solar thermostat
lower than the boiler one. Then the boiler only comes on when the tank has
depleted somewhat. Unfortunately, this would lead to needing a larger
cylinder, as you could only rely on there being hot water above the boiler
stat.

If you don't like the colander effect, you might get away with T-ing off
from fewer flanges, although you should pay attention to mixing pumped and
unpumped circuits in this configuration as unpumped circuits are sensitive
to neutral points and might get reverse or parasitic circulation.

And any ideas where the best online places I can use to get the basic
parts?

You could use your existing tank if large enough, but otherwise pretty much
any cylinder will do. I'd buy an indirect one. Even if you don't use the
coil now, you may wish to use one in the future and it will do no harm. You
can get hot water cylinders anywhere, really.

The plate exchangers are available from GEA Ecobraze. A 14 plate 100kW is
fine, although you can go for more if you like.

I guess the only issue with a non-pressurised system like this is that
the F&E tank will have to be above the solar panels, but I can worry
about that later...

This can also be solved with an additional heat exchanger and pump (are you
counting the pumps yet?!) or by using the indirect coil if you haven't used
it for the boiler.

(Eg. how many building regs I'll be breaking!!!)

None, provided the cylinder is prefoamed and any gas, oil or electric
heating appliances are thermostatically controlled. Also, if radiators are
driven directly from the heat bank, then their pump needs to be
thermostatically controlled to prevent primary circuit wastage which would
result in the boiler firing when neither central heating or DHW demand it.

Christian.