Solution

26240

First name
Laeticia
School
Woodbridge High School
Country
Age
12

Seven squares generalization:

Phoebe:
inverted C's: n (7)
'downs': 1

Alice:
'alongs: 2n (14)
'downs': n+1 (8)

Luke:
inverted C's: n-1 (6)
squares: 1

Total number of matchsticks for all:
3n+1 (22)