Hey buddy,
your question is difficult as it depends on the hospital. I'v worked in big and small hospitals and in private so have a good idea.
I advocate as do many others that New Grads should go into the public system first and work in a hospital. By doing so you will gain a mass of knowledge and it will only improve your skills in private care. That said don't go and be the only physio in a hospital.
Most hospitals are used to hiring new grads and will have supervision in place - they expect you to be terrible at your job for the first wee while and are there to support you. so you certainly want to choose a hospital that has had new grads before and has a good senior physio who will guide you initially.
Your first question about what would you do in a hospital is really hard to answer because it really depends on the hospital. In the Rural hospital I currently work in I do everything as I'm the only physio. However being such a small hospital anything mildly serious goes to a bigger hospital to get looked after. basically whatever wards there are at the hospital you work those are the places you can work (with some exceptions of course). As an example in my first hospital I worked the Outpatients departement which involved respiratory, obstetric, and musculoskeletal work. Then went to the orthopaedic ward - mostly ensure patients can mobilise safely to return home, giving intial home exercises and referring on for outpatient physio. Then to surgical which was mostly respiratory and mobility based work. I then worked paediatrics and Intensive care. I spent time working in mental health and in ED as well as the obstetric ward. There was of course medical and rehabilitation wards that I didn't get a chance to work on before i left the hospital
The bigger the hospital the more specific the work you'll end up doing... that said, and i might get slapped for this, ward work is generally and most commonly getting people to go for a walk. But it can be as interesting and as varied as you want to make it. You don't have to just walk people, you can be very specific to your patients pathology and treat them as such.
So summarising it's normal for new grads to go into hospitals. For your first hospital I'd suggest one that is used to taking new grads and one that has maybe 6 wards or so, so within 2 years you can rotate right around the hospital. You will often rotate from one ward to the next over 3-4 months.
Hope that helps,
Private is fun, But my opinion is that public is the place to be when you first graduate.
Cheers