As far as I know, there is no way to demolish buildings in one of your provinces except to let an enemy conquer it, and then re-take it.
As for the heir, the only thing you can do is keep checking their age. I believe all heirs age in Spring, and after they turn 16 they will assume command of the first unit made. So be careful of what you train in spring when the heir was 15 the last turn.
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Koga no Goshi
"Nandai"
Since time began
the dead alone know peace.
Life is but melting snow.
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