A week is fine. What matters most is that you don't water immediately after potting them up. Maybe wait another week to start watering. There will be no roots for a few weeks to a few months so any water you put into the soil will only leave through evaporation. I would recommend burying the minimum required for stability (like 1-2cm) so as to avoid leaving too much succulence below ground level. You can plant the big cutting intact but try to find a place for it where it will be safe from passing traffic, as it will tend to go sideways at the slightest provocation until it is well rooted.
Be prepared for your cuttings to sit there apparently doing nothing even after they have properly rooted... new growth may be seasonal and not evident until well into next year. Do not overwater over the winter to avoid further complications due to rot. Consider what may have gone wrong to provoke the initial meltdown, in order to avoid another one. Provide the strongest light you possibly can indoors, like right in front of your sunniest southerly facing window.
