Connection Pro-Mini & ESP8266 using Serial
A) is that true that at boot Serial has to be disconnected?

No, that is not true. However if you are using Serial to communicate on the Pro Mini you will need to disconnect the ESP8266 in order to program the Pro Mini as it will interfere with serial communication to the PC.

B) is there a way that 2 MCU can be connected at all times, including reboot when needed ( such as power failures ) ?

Given that A) is a no, then B) is irrelevant. It will just boot.
The only caveat is that the ESP8266 will squirt some boot messages out of serial as it boots at 74880 baud, so you have to be able to cope with that noise in whatever protocol you design between the two boards.