1. If a player sets off any of your traps you should be able to alert them

2. They should not be able to set a halcyon trap until 24 hours after

That's the way it is now ? ...

It's not. You can't alert a player just for setting off your traps, because I think the game doesn't count setting off a trap as an "offensive action" (which leads to point 2).

pretty sure setting off trap alone can't be alerted , or so says one of my legion mates who tried

Say someone attacks you to get a red badge. You're online and able to retrap and stop them. They wasted null fuses and didn't get a badge. No need for them to be alerted. It's good the way it is with setting off traps not counted as an offensive or alertable action.

setting off traps also doesnt remove any hal traps that the attacker may already have set.

Setting off a trap on another player should be made to remove a halcyon trap and make them unable to use a calming amplifier, I believe personally (although it currently doesn't).