A L (a learner = student)
School = ET-ON (minus ON, "not working")
LATE Gives m?l?s?a for 11 across, which I think is:
M - married
ELI's - man's
SA - (sex) appeal
= MELISSA
Incidentally, for 16a I have DUMP but t could be DAMP?
"Tip about wet soil applied to planting, initially" - D?M?