Michelle,
I think you will find different Hospice organizations have different "rules" for assigning any patients whether they are in a LTC facility or at home.
The hospice that I worked pretty much assigned us geographically. I covered a certain area and any LTC in my area was covered by me. That said, there was a huge amount of flexibility and some nurses really liked going to nursing homes and others hated it. It was not uncommon for one nurse to take a week or more and cover all of the LTC patients (if the areas were close enough).
I have heard that other hospice agencies (probably the larger ones) have designated nurses who cover all of the LTC patients. But I think most places you'd have a mix of patient types.
Lengths of orientation or training too will vary by agency. Some will put you to work the next day with little or no training (not a good system!) and others will require a much longer and clearly defined orientation. Those are great questions for your job interview though.
Good luck!