So I need someone's help figure out 1: I need to find out the exact model of my AMD Ryzen 7 processor
and the exact model of my Radeon RX Vega 10 graphics card.
And 2: I need someone to help me figure out how to update them.
Sounds like you have a laptop 'processor with graphics' model.
Check on the laptop maker product page, or install CPU-Z which should show the processor model.
That 'processor with graphics' model is what you download driver for, there is no separate download for vega 10 graphics.