As per wikipedia: "Peak oil is the theorized point in time when the maximum rate of extraction of petroleum is reached". You can still discover new sources of petroleum after "Peak Oil", but the idea is that you will never find enough to increase the maximum extraction rate.

What we see as consumers is conflated by the fact that there are self-imposed limits on extraction by OPEC designed to raise prices. Due to various political situations, those limits have been slowly removed. When you see predictions of "Peak Oil", often they are based on existing production and not maximum production (and hence are nonsense).

I'm not aware of any literature that attempts to speculate on current maximum production capacity. Probably it exists, but I certainly can't find it. Whether we have hit "Peak Oil" already, or whether it will come in the future, I don't know. A lot of that kind of stuff is politically very sensitive and oil companies/OPEC are understandably reluctant to be straight forward with the data.

Finite resources eventually run out. When you don't know how much you have, it's tempting to assume that because you are finding more, you will continue to find more. There is no real guarantee of that. It's a risky strategy.

EROI has been driven down with every single year. One day it will take more energy to extract it than the energy we receive from it but we won't run out.