- Can the dishwasher pump water out?

Yes.

- Could I set up a waste pipe behind kitchen units to connect into the
main waste?

Yes.

- Presumably this pipe would need to have a drop on it of x amount over
its distance?

Yes. It's quite shallow, though, so you should manage it, unless the sink
waste exits the wall high up.

- Could the dishwaster effectively 'lift' water from its drain up to
the level of this pipe to allow it to then run (via gravity) to the
main drain?

Yes.

- Would all of my wastes (sink, washing machine, dishwasher) connect
into one u-bend or is it acceptable to have more than one?

It is better to have more than one, to prevent cross contamination from
blockage and overflow problems when all appliances pump out simultaneously.

I would put the U-bend and a cut down (so you can mount it high) washing
machine style air break stand pipe at the dishwasher position and then plumb
directly to the outlet after the pipe run, using the sink U-bend only for
the washing machine. (Actually, I'd prefer a washing machine air break for
that, too, but if it ain't broke don't fix it and all that).

Christian.