DD's cats

I cannot see anything wrong except leaving the cellar door open because as you say the little one could fall. Our lot, 3 of them, have the run of the house via a flap. The older 2 do not jump onto the work tops/table. The younger one, still a kitten, does but we just lift him down each time. He is getting the message! Years ago we had a cat who would have a go at anything left on the work tops until we covered everything as a matter of course. I am not sure it is possible to spoil cats really.

Will she know whether you leave the cellar door open or close it?

No Elegran-as long as we remember to unlock cellar door before one of them comes home. They've had a lovely day mooching about in the garden today.
I do want to have a word with about the danger of the cellar being left open in any event-it does have a lock high up so easily done.

Even a child-gate across it would be a good thing - if they don't want it closed the cats could get through that for free access (and as an easy escape route if they were being pestered by DGD.)

Very hard to stop cats pleasing themselves - I've had them for years and yes as the children have grown and left home the current ones are our 'kids' I would think that as they're quite used to going in and out of the cellar via the catflap they'll be fine outside for the day providing they are not in danger of getting onto a road. I would second the idea of a gate on the cellar door though - regardless of the cats comings and goings if the little one was to find the door open they could easily fall down the steps which I would think are not carpeted?

Yes Elegran I had thought of a stair gate and will broach the subject when I can? Wish me luck!

I don't see why any animal needs the run of the house. It's not that I don't like cats. It's just that they're animals. They don't really care as long as they're warm, fed and watered.