First inkling that you’ve won/lost an MP Game?

[Xietor]

you cant cast site searching spells at provinces you do not own.

[llamabeast]

I think Voice of Apsu is the exception Xietor, if I remember correctly.

[ano]

Yes, it's the exception and it's the cheapest way to dispel that dome, I think.
Mind hunt is also rather cheap even despite it may result in feeblemind for one of casting mages (and requires S4 while voice requires W2). There're some other good spells for this purpose but it's important to understand that quality doesn't matter. Only price does.
Also, if you're a blood nation, spamming rains of toads may be a good idea as it costs only 8 slaves and will really hurt if it passes through the dome (and if one of the first castings in the turn sequence passes and dispels the dome, all the latter should hurt too)