We describe two-photon photoassociation (PA) experiments operated in an ultracold gas of metastable $^4$He$^*$ atoms in the $2^3S_1$ state. Atom-molecule dark resonances as well as Raman signals provide information on the exotic molecule in the least bound vibrational $J=2$, $v=14$ state of the $^5\Sigma_g^+$ interaction potential of two spin-polarized metastable atoms. The physical origin of the various two-photon PA signals is first discussed. Their linewidths are interpreted in term of processes limiting the lifetime $\tau$ of the exotic molecule. A value of $\tau=1.4\pm0.3~\mu$s is found, which is discussed in view of two recent calculations of the Penning ionization rate induced by spin-dipole coupling and of the atom-molecule inelastic collisions.