The wording of break clauses is tricky (as illustrated by all the threads on the topic here) and often cause confusion (ditto) for no gain.
As said,...
She doesn't need your agreement, but just to follow the break clause and serve notice appropriately.
Effectively the fixed term is 8 months, not 12....
Not really, as the council determines liability according to statute and will go after whomever is liable according to that.
If LL and T have agreed...
You said the council were "aware that there was a tenant living there". Forgive me, but if there are aware then they do not need anything further......
Well if the council knows for a fact that there was a tenant, then IMO the AST issue is just them trying to find ways to attempt to go after the easy...