Two live and one common wire

It is common for a neutral to be shared by two circuits if they are different phases (see @Harper's comments). Your house was probably built under the 2002 NEC code so it may not require that these circuits share a common trip device. NEC Article 210.4 (B) now considers this a multiwire branch circuit and requires that both ungrounded conductors be equipped with a simultaneous disconnecting means. This is more to protect someone from a shock hazard caused by breaking the neutral and getting caught up in a series hazard between the load side of the neutral and the line side. Basically it makes you or part of you the load.

So yes it is not unusual, but if the circuits do not share a common trip, you should replace them with one that does. Hope this helps stay safe.

Your recessed lights are hooked up in a "switch-loop", identified on this link as the third example (at the bottom): Link to important stuff

The previous poster was trying to say that per code, switch loops are no longer allowed; the 2nd example is now the standard (using 14-3 wiring; has an extra red wire). What happened is not a crime. Switch loops were used by electricians as a smart way to wire; whenever power goes directly to a light (and not a switch before the light), using the white neutral as a power allows the switch to work without having to string the extra length of wire. Today's code prefers "a safer" approach with 14-3 wiring, although it doesn't really look safer.

With the fan switch, you should pull out the wiring further to find where the white wire went. With two separate breakers, it shouldn't be hooked to the recessed lights, or it will trip the breaker.