Essentially all energy absorbed by CO2 molecules in troposphere is very rapidly released as heat of atmosphere. Conversely heat of atmosphere maintains continuously so many CO2 molecules in excited state that these molecules emit approximately as energy as CO2 absorbs. The small difference between absorbed and emitted energy heats or cools atmosphere at that point. Throughout the troposphere the emitted energy is slightly higher than the absorbed energy, because convection provides part of the incoming energy.
The difference between emitted and absorbed energy is highest at low altitudes and goes down to zero at tropopause. This condition determines the altitude of the troposphere.
Answering your questions:
(1) most of radiation out to space is from troposphere and a large part of that is from the uppermost part of troposphere not far from tropopause.
(2) no, if you refer to thermal expansion of air. The main change is that a larger part of air will be part of troposphere rather than stratosphere.
(3) the above answers that as well
(4) here we come back to the issues discussed in the first and second paragraph above. More CO2 makes the difference between emitted and absorbed radiation larger at low altitudes. Therefore a larger vertical distance is needed to reach zero difference. The temperature is lower there, because the altitude is higher and the lapse rate has a longer distance to make temperature lower.
(5) that means, indeed, that there’s less cooling radiation until the surface and the atmosphere has warmed up enough to compensate for nearly effect, which continues for several decades and even longer at some level. (After this warming the total amount is the same as before, but it’s composition is different.)