Since all of the Detect spells have a duration of Concentration, it seems to me like you have to concentrate to gain a benefit from them. If the Night Hag concentrates for 1 round, she can use any of her detect spells without having to cast it, but she doesn't get any information without concentrating. The difference here between continuous and at will is that the continuous version doesn't provoke an attack of opportunity. I don't think there's a solid rule on this, but I feel like this solution fits the normal behavior of the spells best.

A spell is resolved - and the target is determined - when the spell comes into effect, not when spellcasting is "starting".

So in the example the sorcerer could still cast the spell, just another target would be determined if they are no longer aware of where the wizard is. The only way to stop the spell being cast (Spell resistance, saving throws, etc are another matter) would be to counterspell or disrupt (Concentration checks) the spell itself - removing the (intended) target before the spell is complete simply means that the caster (the sorcerer in this case) is free to choose a new target.

Ie. Even though the sorcerer had taunted the wizard the spell target hadn't yet been determined.

This is usually most relevant when a spell takes more than a simple action to cast (such as sleep, a one round to cast spell) but when reactionary effects get in the way spellcasters can still choose their target if their original one vanishes before their spell can take effect.

It's detailed in the Casting Time section of the Magic rules of Pathfinder, but the most important line of it is:

You make all pertinent decisions about a spell (range, target, area, effect, version, and so forth) when the spell comes into effect.

So, in the fraction of a moment where the wizard teleports away the spell's effect has not been determined - the wizard hasn't made a saving throw. So the sorcerer is still free to target anyone else they want. If there are no relevant targets of course (say, charm animal and all the animals vanish into the ether on a joyride) then obviously the spell will fail through lack of targets.