Am I able to move dependents prior to PCS date on an unaccompanied tour?

Yes, at your own expense. You can move your family worldwide at your own expense. You could talk to your landlord and ask to stay a little longer paying by month.

You can but it will cost you. I suggest talking to your lanlord ASAP and request if you and your family can continue living there on a month-month basis. You can also call ahead to your new duty station’s housing office and speak with them on the matter and see what your options are. Good luck.

Your family can't move without you and you can't report in prior to actually physically reporting in.

The best thing and mature thing, for you to do is talk to your landlord and tell them when you'll move, plus give them a copy of your orders.
The douche bag move is to wait till you need to move and break your lease with your orders giving 30 days notice