Core. Home is a second component, hence the different version number. So you have a newer version of the core than when that feature was released, so good to go.
Via the new terminal button (arrow) or the quick access list (PIO icon then New Terminal).
#3) When clicking the icon Run Task at the lower left it pull up a list of options we can click on like Build, Check, Clean and so on. Why not put menuconfig in that list as well, or an icon for it ?
The quick access icons don’t change depending on what platform you use… so adding a ‘menuconfig’ icon would. Better to either add it to the run task list, which AFAIK is the same as the list of project tasks shown when you click on PIO icon (#1 in the screenshot above). In other words, I agree that a menuconfig option should be added to that list targeting on the espressif32/esp-idf, which should then make it a ‘run task’ option also.