The first question you pose, regarding carrying capacity, can only be answered in terms of quality of life. In turn the question begs another: how can humanity be supported on Earth?

This is, in fact, the key question, as how support is created determines how much of it there is. For example, to provide grain from a field crop, one can provide a little more if one includes all the seed for next year to consumers instead. Thereafter there's no more grain available.

If support is only provided by commercial farms owned by megacorporations, who spend no little attention on lobbying, lawfare, and marketing, which help it to crush competition and gain a monopoly, so much may be supported. If different mechanisms are used, or banned, or prevented from being options by resource depletion, different answers to the question are arrived at.

There really is no actual limit to how many people can live well on Earth. Given aquaponics and personal control of food production via in home vertical farming, neither is there any limit on the quality of that sustenance. The limits presently are effects of the socioeconomic systems presently employed, and those are selected not for the benefit of consumers, but for investors.