Do I have to provide VCC to every VCC pin on Atmega32u4 MCU?
Yes you need to supply power to each Vcc pin and NO you can't feed power through the chip to other devices, LEDs etc.

The multiple VCC pins provide proper power distribution around the wafer. If you only use one a) it may not work, and b) that one pin may not be able to carry the max current and the bonding wire may burn out.

If you attempt to use the other Vcc pins as power routing, you are routing ALL the power through the chip. That just makes things worse. Further, any switching of those devices would cause current spikes in the Micro.

Addition: You ALSO need to add decoupling capacitors close to each of those Vcc pins.

Addition 2: You did not ask, but the same goes for all the ground pins.