are you allowed to hit the home button on your switch and change the time manually or do you have to set it before the run starts. I am not the most consistent so it would be helpful to change time mid run if that is allowed

2 more questions as well. my switch is using version 15.0.1 so am i not allowed to submit my runs? also do i need a capture card or can i just stick a camera infront of my tv.

"As of June 23rd, 2021 Switch FW versions older than 10.0 are prohibited"

15.0.1 is not older than 10.0.

i read the rules wrong on the FW. what about exiting the game to change time?

Changing the time mid-run is allowed, and you don't need to record with a capture card for the video to be verifiable, camera footage is fine as long as it is clear enough.