  We spectroscopically investigate the hyperfine, rotational and Zeeman
structure of the vibrational levels $\text{v}'=0$, $7$, $13$ within the
electronically excited $c^3\Sigma_g^+$ state of $^{87}\text{Rb}_2$ for magnetic
fields of up to $1000\,\text{G}$. As spectroscopic methods we use short-range
photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold
molecules which have been previously prepared in several well-defined quantum
states of the $a^3\Sigma_u^+$ potential. As a byproduct, we present optical
two-photon transfer of weakly bound Feshbach molecules into $a^3\Sigma_u^+$,
$\text{v}=0$ levels featuring different nuclear spin quantum numbers. A simple
model reproduces well the molecular level structures of the $c^3\Sigma_g^+$
vibrational states and provides a consistent assignment of the measured
resonance lines. Furthermore, the model can be used to predict the relative
transition strengths of the lines. From fits to the data we extract for each
vibrational level the rotational constant, the effective spin-spin interaction
constant, as well as the Fermi contact parameter and (for the first time) the
anisotropic hyperfine constant. In an alternative approach, we perform
coupled-channel calculations where we fit the relevant potential energy curves,
spin-orbit interactions and hyperfine functions. The calculations reproduce the
measured hyperfine level term frequencies with an average uncertainty of
$\pm9\:$MHz, similar as for the simple model. From these fits we obtain a
section of the potential energy curve for the $c^3\Sigma_g^+$ state which can
be used for predicting the level structure for the vibrational manifold
$\text{v}'=0$ to $13$ of this electronic state.
