本来は契約書が必要だと思いますが働くところによって(特に飲食店等)契約書とか無いところもあります。(=違法な労働を強制するとは限りません)
http://www.labour.gov.bc.ca/esb/esaguide/に日本でいう労働基準法が説明してあります。
祝日に関しては以下のようになっています。祝日手当てをもらうには働いて30日以上経っていること、祝日の直前から30日間のうち15日以上勤務していることが条件です。トピ主さんの場合、毎週週4日働いたとしたら16日間は勤務したことになるので手当ての対象になりますが週3回の週が2週、4回が2週だけだだと15日に満たないので対象となりません。
To qualify for statutory holiday pay employees must:
Have been employed for at least 30 calendar days,
And
Have worked on at least 15 of the 30 days before the statutory holiday.*
*Employees who worked under an averaging agreement any time in the 30 days before the statutory holiday do not have to meet the 15-day minimum.
Qualified employees who are given a day off on a statutory holiday must be paid an average day’s pay.
Qualified employees who work on a statutory holiday must be paid:
Time-and-a-half for the first 12 hours worked and double-time after 12 hours
Plus
An average day’s pay.
An average day’s pay is the total regular earnings divided by the number of days worked in the previous 30 calendar days.
Regular earnings include wages and vacation pay received for vacations taken, but does not include overtime pay.
Days worked includes all days where wages were earned as well as any days of annual vacation taken in the 30 calendar days before the statutory holiday.
Employers and a majority of employees can agree to substitute another day for a statutory holiday. The substitute day must be treated the same as a statutory holiday.