Based on calorimetry and dielectric spectroscopy, the influence of dopants as well as H/D-isotope substitution on the dynamics and thermodynamics of expanded high-density amorphous ice (eHDA) is studied. We find that dopants do not significantly alter the phase behavior, the dielectric relaxation times, and the calorimetric glass transition of eHDA. These observations starkly contrast those made for crystalline ices such as ice I h , ice V, ice VI, and ice XII, where suitable dopants enhance the dielectric dynamics by several orders of magnitude and can trigger hydrogen order-disorder transitions, then taking place below the orientational glass transition temperature of undoped samples. This conspicuous contrast to the behavior of crystalline ices strongly argues against point-defect dynamics in amorphous ices and against a previously suggested "crystallinelike" nature of the amorphous ices. Furthermore, H/D substitution also does not affect the calorimetric glass transition in eHDA much, whereas for crystalline ices, the heat capacity increase at the glass transition is roughly halved. In addition, the H/D-isotope shift of the glass transition onset is much larger for crystalline ices than it is for amorphous ices. This observation favors the notion of eHDA's glass transition as a glass-to-liquid transition and is evidence against a mere molecular-reorientation unfreezing at water's second glass transition. Comparing the isotope effect on activation energies for dielectric relaxation with ice V suggests that in amorphous ice water molecules move translationally above T g. Thus, the present work strongly supports that above this glass transition, water does indeed exist in its contested high-density liquid state.