The bromine tabs are effective until they are fully dissolved, but their rate of dissolving in terms of amount of bromine getting into the water gets lower when the pucks are much smaller so you usually add another puck before the first one goes away. You do not discard smaller pucks.
If you properly disinfect/oxidize your spa, you should not need to use a clarifier. With bromine, you may need to shock on occasion with chlorine to keep the water clear.