If she is in Year 1 (about to go into Year 2) then the infant class size rule applies (ie by law they cannot take additional children if they already have 30 per class). If the school know they already have 30 children per class in the current Year 1, maybe that's why they said there is no chance but it is up to the LEA to add you to the waiting list and sort out the application process.
Probably just nursery admissions. And possibly the admin associated with new children starting Reception. But they will have been allocated places by the LEA.
Nursery places will most likely have been allocated already at this stage in the year - if not fill in the nursery form for DD2 - you can always decline the place later if you decide you don't want one. Put DD1 on the waiting list with the LEA(depends on the school/area obviously but DC's school had lots of children leave at the end of Y1). If DD1 doesn't get a place in school you can then decide what to do with DD2.