With regards to your question 1, I reproduced the behavior you described on our ADV7630 evaluation board. However, to be honest, since ADV7630 only provides a mux (i.e. no CP), it can only output the type of signal that is input. In other words, if the input signal is DVI, the output signal will be DVI. If the input signal is HDMI, the output signal is HDMI. I see the same behavior on ADV7625 when it is configured for mux mode rather than non-mux-mode.
With regards to your question 2, I also reproduced the behavior you described on our ADV7630 evaluation board. On the ADV7625 evaluation board, the HDMI_MODE bit appears to work correctly. Since ADV7630 documentation does not include the HDMI_MODE_RX1_RAW register, I'm guessing that HDMI_MODE detection is not present. But since the ADV7630 operates in mux-mode, I'm not sure whether detection is necessary. I will ask the ADV7630 experts about this.
-Matt