Shouldn't a variable start with a lowercase like "personAge"?

Answer 1

The starting of a variable name with a lower case and then uppercase for each beginning word after is called CamelCase. Ex. firstName or studentLetterGrade. There's also Pascal Case which uses an uppercase letter for every word. Ex. FirstName or StudenLetterGrade. It's up to you which one you choose.

Answer 2

use camelCase for naming backing fields, local variables and parameters. use PascalCase for naming Methods and Properties