I think picking a new deputy is only in Part 2, because it’s announced during a cutscene that happens on Day 5. As for the killing a clan member, it depends on who you kill and how you kill them. There’s a clan meeting called if you kill someone with a Poisoned Mouse, but other than that CedarClan cats generally won’t react (unless you have a low reputation, which will happen if you kill cats and are not going out of your way to hunt more, as you get kicked out for having low reputation).