I think it was Millet who was talking about pot shape-
shallow wide pots actually stay more wet, tall pots drain better. Ive had some herbs in a bowl type pot and theyve gotten soupy
you still dont want to water either type of pot too often, inside, i was only watering my 3gal kumquat every week or more in the winter.
I have no idea about the other questions- if the plants were in the shade first, theyre probably a bit stressed. if your greenhouse is hotter than where they were, theyre probably stressed.
good luck!