Student or Learner
"Being foster parents, the Webbs/Webb’s had a number of children under their roof, including kids they adopted, and many of them..."
It works like any other plural. Their surname is Webb. There is more than one person in the family so they are "the Webbs". Using an apostrophe would suggest the possessive which is unnecessary in your sentence.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.