Do you have to pay prorated rent if you physically haven't moved in the home yet?

Yes, you pay rents from the time you agreed to rent the premises, even if you have not taken occupancy. If you decide not to move in for three months, should the landlord not receive rent income for that period ? Or course he deserves that income.

Yes. You owe rent from the day you sign the lease OR whatever date your LL agrees to allow your tenancy to begin.

Whenever you actually move in is up to you.

You and the landlord decide the move in date and when to pay.

Also there should not be a prorated rent, it should start from a specific date.