Applications of incidences theory to some triple exponential sums

Let $\chi$ be a nonprincipal multiplicative character modulo a prime number $p$. Using the incidences theory over $\mathbf{F}_p\times \mathbf{F}_p \times \mathbf{F}_p$, we find new bounds for the sums
\begin{multline*} \sum\limits_{a\in A,\,b\in B,\,c\in C} \chi(a+b+c), \sum\limits_{a\in A,\,b\in B,\,c\in C,\,d\in D} \chi (a+b+cd),\quad \sum\limits_{a\in A,\,b\in B,\,c\in C,\,d\in D} \chi (a+b(c+d)) \end{multline*}
over arbitrary sets, and for a trinomial sum
$$ \sum_x \chi(x) e_p (ax^k +bx^m + cx^n) \,. $$