When and where is the atmospheric greenhouse effect strongest?
It is strongest in the arctics,most radiation from this area will be long wave infra red and long wave infra red is absorbed and reflected by the climate gases in the atmosphere.

A large part of the heat from the sun is reflected by snow and ice,But as the snow and ice melts more heat is absorbed by the water in the ocean the effect of this is larger in the arctic(floatng ice)than it is in the antarctic(more ice on land and takes longer to melt)

Link https://en.wikipedia.org/wiki/Infrared

At the areas closer to equator the heating is higher so a larger amount of the radiation will be at a shorter wavelenght,And a larger portion of this will escape to space and not be stoped by the atmosphere.

The equator will heat up less than the arctics simply as a result of the shorter wavelenght in infrared radiation.

The winters will warm faster than the summers in the arctics and this too is a result of the longwave infrared radiation in the winter and the shorter wavelenght(hot summer).

The nights do warm faster than the days too as a result of longwave radiation at night(colder)and shorter wavelenght in the day(hotter)

The earth will keep getting warmer until a new equiriblium is reached where incomming and outgoing heat will be in balance(if we stop the realease of greenhouse gasses today the earth will keep on getting hotter for atleast 50-100 years).