Casters do retain connection to their spells, in the sense that the caster, and no other, can end a duration spell before the end of it's duration via one round of concentration. (P84 of RMC spell law, similar note in RMSS)
The caster has to be within the radius of original casting, or within sensing range of the spell's current effects.
That places a rule context stating that at least spells with durations are still connected to the caster in some manner.
There is no rule anywhere saying that connection tells the caster anything, though as GM I'd likely allow a caster to "Check" a duration spell with no overt effects by concentration, then NOT cancelling it. (Is my ward on that door still active? I walk 10 from the door and concentrate a moment, yes it's still there, or no it's not).
I dunno that you'd sense a failed dispel on your fly, any more than you'd notice any other such spell being cast on a target other than you specifically. . .it's a tricky call though, as the fly spell is on the caster, so in some sense they are the target. . .GM call I'd say, as the rules are not firmly either direction.
Spells with a duration of "-" would seem to be the fire-and-forget kind.
Insofar as I am aware, spells are not as subtle as all that, unless specifically stated. . .and can be used in context. . .
i.e. if I ignite the table in front of you, it's magic, if I ignite the wall next to the fireplace while nobody is paying attention, likely people will assume that the fireplace started the fire.
I sleep 5 guards late at night when they are drowsy and half asleep, sneak past, and move on, they might assume they fell asleep normally. . .I sleep 5 alert guards who are in the middle of a conversation then likely they'll know they were magically effected as they literally drop mid sentence from their feet to the ground.
Charm doesn't delete memories, and unless you use it on a good friend, I'd assume the sensation of thinking someone is a good friend will feel very wrong afterward in context of your memories. . . might slip past if the target is drunk and very friendly, but in almost any other context I'd think the "I met this stranger and he was my bestest friend" would seem quite wrong in retrospect.