I noticed that a beacon didn't detect it's own transmission. Did that mean that the beacon alternate between the transmission and the scan, and turn off the transmission when it scan? If yes, did that affect the transmission rate, even a little bit, if I am using a transmission rate of 10Hz ?
No, transmission does not affect scanning. Bluetooth radios are designed to both scan on multiple channels (slightly different frequencies) and transmit on those same channels. There is a channel hopping mechanism that governs this.
Devices by design are not supposed to pick up their own advertisements in scans. This is a separate issue than described above.