Well, you can't take someone with you, otherwise it wouldn't be a solo assassin
It depends, if you have the settings set on 8 hours of rest, then all your Hp may not be recovered, depending on how much damage you've taken. If you've set it for 'Sleep until healed' then you'll have full Hp when you wake up (depends if beasties ambush you or not).
You don't necessarily need a cleric, just remember to pick up or keep plenty of healing potions on hand and you'll be fine.