Racks don't need power. Distribution devices do to power the devices but not the rack itself. Confused at your question.
It's simple :s?
You have a rack which devices screw into.
Each rack can have 2 power strips (pdu) so you can power devices like you would power your pc...
In it's most basic form, yes.
Get a managed PDU and it will have an Ethernet port. That lets you do various tasks such as look at power consumption and remotely power off/on individual sockets to reboot hung devices. Ideal for equipment you might need to reboot but don't have on-site people to do it.
In a small environment, it could go directly into a UPS in the same rack. Or, if the equipment isn't super important to keep going during a power-cut, directly into the mains.
In larger DCs, the UPSs are shared between multiple racks.