Not for the lawn area - the ashes can be spread around the garden, but don't use too much round any one plant - depending on the wood you've burnt and the current ph of your soil, it may alter the ph, particularly around acid loving plants.
That area mapped out in the pic looks good, I like the paving. I haven't used either of the products you mention, but so long as they contain short leaved rye grass as well as other grass seeds, they should do the job just fine.

The Family Lawn seed will be a mix intended for people to walk on as opposed to one purely for looking beautiful, and these mixes usually do contain rye grass which is a tough one. It often says on the pack what the mix is.
As Bamboo says, it looks very nice indeed. Good luck with your lawn.

You have done really well with the prep - the soil looks flat but not compact, so the lawn will look great quickly. It looks a little sandy, if so you can add some compost later on to add nutrients and stop the water draining away.

Hi
Looks lovely already, peronaly I would put the feed to one side for now or use it on your other lawns that you have.
I never like to overfeed a new lawn and never do for the first season as I like the roots to get into the soil looking for food , I would though keep a eye on watering new grass can die with in a mater of days especialy in the spring with the drying winds , depending how it does in the summer I would give a Autumn feed .

Hope you find useful

Gnarly g