the 12 hours in the previous 24 months
It is 12 Hours
and 1 Hour with an Instructor.
Total 13 Hours.
If your LAPL is not valid then you cannot exercise it's Privileges. But if you hold another
valid Licence (eg NPPL) then you can fly on those Privileges until the experience gained renders your LAPL valid again.
build the 12hours under the supervision of a ato
The rules don't state nor, as far as I can see, even imply that an ATO needs to be involved. However it would be a very brave Instructor who authorised an 'unlicenced' pilot to fly solo outside the auspices of a flying school. This would also have to be authorised by an FI, I cannot see this falling within the privileges of a CRI.