I am on because and I usually get my period on Wednesday through Saturday like clockwork. I didn't start bleeding until Saturday and with almost no cramps. Its early Sunday morning and the light flow has stopped. Could I be pregnant?

Of course you realize that no birth control is 100 percent effective and women get pregnant while using birth control at times. So if you are sexually active of course you could be pregnant.

And no, periods do not come normally like that. They are normally certain amounts of days, 28 day cycle, or 30 day cycle. So they should be coming according to days, not a certain day of the week. If you always get it on a Wed or specific day, that does not seem right.

But if you are late, you have to wait till you are about 14 days late to do a pregnancy test

Actually you can time your cycle by the day of the week when using birth control dependent upon when you start taking the placebo pills.

With that said, yes, pregnancy is a possibility if you are having intercourse as no form of birth control is 100% effective aside from abstinence.

But when taking birth control pills, it is a certain number of days, some months it will have to be Monday or Tuesday, not always on a certain day of week?

Of course, as some months have 31 days and others have 30. The OP said usually, not always.