Assuming you have enough bandwidth you can run many cameras down a single link. You will just need the poe switch to be at the end of the cox run once its converted to Ethernet
You could use a control panel for this and adjust the bell time or a timer relay eg
https://www.securitywarehouse.co.uk/catalog/intruder-alarm-c-36/intruder-alarm-ancillaries-c-36_46/tkc-160-precision-timer-p-2664.html