1. For humans, you could theoretically repopulate the planet with just two fertile individuals, but that would leave no room for accidents or anything of the sort so it would be very, very risky. In order to make that work, the couple would have to have a lot of children and their children would have to have a lot of children, etc. They would have to arrange it so that people had children with different people (so you sleep with all of your siblings!) in order to maximize genetic diversity. There would probably be a lot of children with genetic issues, but as long as each generation is getting more than two to survive and everyone survives long enough to have a lot of children, then the population will rebound. The species might end up different than from before the population bottleneck, but it could survive.

If you want to avoid inbreeding (or at least keep it to cousins) and leave room for accidental deaths of people who are fertile or haven’t reproduced then you just increase the number of people. Exactly how many depends on how much you want to guarantee survival. 5,000 would almost certainly be enough provided there isn’t a catastrophic disaster or plague or something of that nature. I don’t think there’s a point where it goes from “not okay” to “okay”, though. It just gets less risky for each person you add.

For biological conservationists, the minimum number of individuals required to maintain a species is called the minimum viable population (MVP). The MVP for most species in the wild is around 5,000 without human intervention. If you include human intervention, a study on pandas showed that with 50 pandas, there was a 70% probability of survival.