Could brown discharge/irregular bleeding week before placebos, and almost nothing the next week mean birth control is stopping my period?

Yes: Frequently the pill can cause shorter and lighter periods - usually a desireable side effect. Many women may notice an irregular and/or very light or even no menses while on the pill. This is not generally cause for alarm - assuming that you aren't missing taking the pill on schedule. There is no evidence that the pill's effectiveness is reduced at this time, as well.