USART, SPI or Bit-Bang for the continuous transfer of bytes without inserted extra bits
Are both these statements true? 


Neither of those statements are true.

SPI never inserts extra bits. That would break everything if it did. What you are probably seeing (or think you are seeing) is a delay between bytes being sent. That delay is irrelevant, since the data is only ever sampled on an edge of the clock signal (which edge depends on the mode of the SPI communication) and with no clock edge in that delay period there is no data.

USART in synchronous mode is SPI. There are no start or stop bits in synchronous mode, since the clock is used to synchronise the communication rather than needing start or stop bits.