With a car alternator that puts out 14.4 volts, it should never reach a point for the bms to activate at 14.6 volts, especially while engine is running and using power. The only problem would be if the battery were to go out of balance then the bms will activate, but since the car is running the alternator will have a load that it can output its power to. I don't understand how the voltage regulator works in a car environment but that might be something that prevents voltage surges.
To your number 2 question, with solar charge controller, if the bms activates, that is very bad. You will get voltage surges. Voltage surges can reach over 20 volts which will destroy any 12 volt devices that can't handle such overvoltage. The only solar charge controller that i have seen that actually states that it can handle a bms activating without causing voltage surges is the makeskyblue 60 amp mppt Below is the note on bms activating while connected to solar.
" 3. The advanced application for V118 50A and 60A:If your load device is shorted or over-current, the controller will have output short-circuit, protection and close the output. When you disconnect the load and press ENT over 5 seconds, then output will turn on again. Please note the 30A and 40A don't have this function. The MPPT output of the battery voltage will not rise suddenly, and the controller doesn't cause the output voltage to overshoot through the BMS protection board.
By the way, the charging voltage of V118 version can be set from 12V to 17V compare to the fake products is from 13.5V to 17V. The discharge voltage can be set from 9.8V to 14V.
I always look at controller manuals to check how it reacts to a bms activating, and most manuals don't mention it. I don't know how the victron would react but I would be hesitant to use it on lithium unless I knew for sure how it would behave. I know from reading other forums that battleborns will cause voltage surges when the bms activates on solar, any lithium battery that uses mosfet bms will cause voltage surges if activated while on solar.