Learn Finnish: Minä teen tämän työvuoron kollegan sijasta. - I am doing this work shift instead of the colleague.

Because it is governed by the postposition sijasta (instead of). Like most Finnish postpositions, sijasta requires the noun that precedes it to be in the genitive case. Therefore, the base word kollega becomes kollegan.

Could I use puolesta instead of sijasta here? How would it change the meaning?

Yes, you could say kollegan puolesta. While sijasta specifically means you are doing the shift instead of them (taking their place as a substitute), puolesta means you are doing it on their behalf or for their benefit. In this context, both often result in the exact same real-world action, but the nuance shifts from mere replacement to doing someone a favor.

Why is the object tämän työvuoron in the genitive-looking accusative case rather than the partitive?

Because the action is viewed as a complete whole. By saying teen tämän työvuoron, you are stating that you are going to complete the entire shift. If you used the partitive (teen tätä työvuoroa), it would imply an ongoing, continuous, or incomplete action, such as currently being in the middle of working the shift.

What is the literal building block behind the word sijasta?