Mister Snooze:
Yes, 24 hearts is max.
You don't search caves and holes for the Mirror Shield. You search suspicious dead ends on the overworld that when you step into, you get teleported to a part of the Fairy Cave. Find all these fairy warps, then enter the Fairy Cave through its main entrance to eventually find the Mirror Shield.
I have a list of fairy warp spots if you really get stuck with them.
Arieltap:
You have the boss key? But then you probably were everywhere where you need to and also seen the overworld floor, since you got the 2nd dungeon item from there, required to get the boss key, which you say you have. Just go back to that overworld floor (remember, from the middle of Chain Reaction) and use the boss key to get to near the end.
I don't recall map or compass being in there.
The Mirror Shield is optional, but the Moon-adorned Cane of Byrna room requires that, too. Not required to get any of the endings, but if you find almost all optional items, that comes with good reward in the END.
Night and Day? The only tower where I recall a night/day system was the Rotting Tower, but even that had night/day only outside. The Tower of Power doesn't have that.
The further the fairy switch is, the higher level area the warp is in. If there are extra details around the switch, that also helps to pinpoint the location.
I have a list of fairy warp spots if you really get stuck with them.