  We present a combined experimental and theoretical study of highly charged
and excited electron-hole complexes in strain-free (111) GaAs/AlGaAs quantum
dots grown by droplet epitaxy. We address the complexes with one of the charge
carriers residing in the excited state, namely, the ``hot'' trions X$^{-*}$ and
X$^{+*}$, and the doubly negatively charged exciton X$^{2-}$. Our
magneto-photoluminescence experiments performed on single quantum dots in the
Faraday geometry uncover characteristic emission patterns for each excited
electron-hole complex, which are very different from the photoluminescence
spectra observed in (001)-grown quantum dots. We present a detailed theory of
the fine structure and magneto-photoluminescence spectra of X$^{-*}$, X$^{+*}$
and X$^{2-}$ complexes, governed by the interplay between the electron-hole
Coulomb exchange interaction and the heavy-hole mixing, characteristic for
these quantum dots with a trigonal symmetry. Comparison between experiment and
theory of the magneto-photoluminescence allows for precise charge state
identification, as well as extraction of electron-hole exchange interaction
constants and $g$-factors for the charge carriers occupying excited states.
