When I make rice for sushi, I season it with sugar, salt, rice vinegar, and mirin. I'm never sure if I should add these at the beginning or near the end of cooking the rice. Does it matter when I add these seasonings?
You should add the seasoning at the end of cooking the rice.
Actually normally I let my rice cool down for 10-15 minutes and transfer it to a large mixing bowl before mixing the seasoning with my rice.
I do not think it matters when you add the salt BUT the wet ingredients (including sugar) should be added after the water has been absorbed by the rice.
You should drizzle your rice vinegar/sugar/salt/mirin reduction a little at a time while the rice is spread to cool. Drizzle a little, then fold. Repeat until your reduction is gone and continue to let your rice cool until ready to use.
Don't try to store leftover rice. It's a petri dish for bacteria that cause food poisoning.