Kan extensions specify the adjoint structures between $\mathbf{Sets^{C^{op}}}$ and $\mathbf{Sets^{D^{op}}}$, where there exists a functor $f:\mathbf{C} \to \mathbf{D}$ and $\mathbf{C}$ and $\mathbf{D}$ are small categories. $(\infty,1)$-Kan extension is studied in higher topos theory, model categories, and homotopy theory such as homotopy Kan extensions.
A special case is the locally cartesian closed category. The triple adjunctions can be $\sum_f \dashv f^{*} \dashv \prod_f$.
My questions:
1.Are the above left and right adjoint of $f^{*}$ unique ? Or there are other such adjoint compositions for $f^{*}$ ?
2.There are examples in nlab. But are there other cases other than $\mathbf{Sets^{I}}$ and $\mathbf{Sets/I}$ known with such structures ?
3.What are higher analogies of special cases for the adjointness relations ?