what is the age group of the room your DD is in (sorry if you mentioned already I didnt see it)

Biting is a lot different if its a 3year old than say an 18 month old. Younger kids then to do it more out of frustration in not being able toe xpress themselves, where as old children its a lot more premeditated.

In both cases they should notify you (and to whomever said they should notify you immediately - I havent found its my experience thats thats normal unless its bad enough that they want you to collect your child, or want permission to give them pain relief) via the accident book that they're required to maintain.

The child who did the biting/hitting's parents should also be informed as they are required to sign the incnident/accident report also.
DS was something of a biter from about 15-18 months, and it was horrible. I dreaded picking him up from creche becuase thered be an accident report at least 50% of the time.

It's not acceptable at all that the director and the staff member gave you conflicting reports on how the split lip came about, and for that one I would have expected a phone call - I know I've had them before when DS bit his lip at creche once.

I'd definitely go in unannounced a couple of times to see whats happening, but also ask to see their policy on behaviour management, they should have it available and have to let you look at it.

From our experience I can tell you the staff really were helping us to work through it and sort out strategies to manage DS' behaviour, and they provided us with a lot of relaly helpful resources - it may be that the staff memeber didnt express themslevs adequately, or was worried about privacy issues or something like that