This doesn't do anything, == is for making comparisons
millis() == 0;
millis() returns a value - don't believe you can set it with millis() = 0;
make these unsigned long and put UL after the number.
long day = 86460000; // 86400 sec/day adjusted for the atmega328 clock
long hour = 3602500; // 3600 sec/hour " "
long minute = 60041; // 60 sec/min " "
long second = 1000; // 1000 millis/sec, unadjusted
long alarmTime = 60041;
make any variables having to do with millis() unsigned long
this needs == for comparison
if (alarmTime = timeNow){
otherwise you are setting alarmTime equal to timeNow, which apparantly equates to being True within the if()
same here
if (boolean alarmisON = true){