Your health regenerates if you get into battles after you get the death warning, it just will max out at lower and lower numbers (max health goes to 90%, then 80%, etc) until you eventually die. You can still fight if you want to. And yes, once you die, a pop-up window comes up for you to choose which character you want to take over the clan. You don't need to stash your inventory, it just goes into the inventory once MC dies and you can reassign to whoever your heir is (unless the update changed this). And sometimes, it's better to get an unskilled heir so you can try different perks.
And don't feel bad, I've had my mc die of old age too. So what if I'm a "slow player?"