I am no expert but from what I read, the air layer shoot was supported by the mother plant mostly before you cut. Once you cut, it has to switch to the new air layer root, which is small relative to the mother's. People usually trim the leaves and/or the shoots to help the new air layer adjust. You can let it do the job naturally (through shedding ) but don't stress it in the hot summer full sun in the meanwhile.
Roots coming out so soon means the pot may be too small for it to begin with. The brown spots are fungal disease from overwatering. Just pull those leaves out or plant will shed them eventually. I would keep the plant in indirect sun, up pot to the next size, which gives it a more stable environment(without going through the daily wet & dry cycle) and try to avoid overwatering by checking the soil moisture first before you water.
The other thing I learnt was black pot can get hot in the sun (by measuring the soil temperature 1" from the edge of the pot) and it is especially a problem for a small pot relative to the larger plant. Use something white or reflective to wrap the pot when it is ready to receive the full sun and add some mulch on top to slow moisture evaporation if the mix is high porosity. Obviously, these two have to wait till the brown spot problem gone and the plant stabilize to indirect sunlight.