“This penalty” is -1 per 2 points of ability damage. So the character has lost 18 hp off their maximum. So their hp max is 7 and has taken 23 points of damage. Oh, and has a Con score of 8 thanks to 1 point of drain, so... yep, that is one seriously dead character.
They took a full 6 points of Con damage, bringing their Con to 3 (-4 penalty). 1 is drain because they didn't make an extra save.
So I'm unsure as to how their HP should be adjusted. In the CRB regarding constitution damage it says 'multiply your total Hit Dice by this penalty and subtract that amount...'. Not sure what 'this penalty' refers to - the number of constitution points lost (which is 6) or their current constitution penalty (4)?
Ability damage does not reduce your score in any way. Instead, every 2 points of ability damage gives you a -1 penalty on things. That is the penalty the rules talk about. So in your case, you have 5 points of Constitution damage and 1 point of Constitution drain. That reduces your Con from 9 to 8 (from the drain), then gives you a further -2 penalty on any Constitution related checks (from the damage).
The drain isn't enough to modify your hit points. The damage reduces both your maximum and current hit points by 2x your hit dice, or a total of 12 in your case. If he only had 2 hit points left before that, this drops you to -10 and since that is below your negative constitution score (-8 in this case), you are dead.
Additionally, hypothetically, does the 1d6 Con damage/drain happen every day until the character makes two saves/dies?
Yes. Note that the 2 saves must be back to back. You can't succeed on one, then fail one, then succeed on one. You must succeed on 2 saves in a row.
Also note that demon fever has an onset time of 1 day. You don't take the damage immediately upon contracting the disease. That means there would of been time to heal up some before the disease dropped your hitpoints, possibly avoiding death.
"The only exception to this is your Constitution score. If the damage to your Constitution is equal to or greater than your Constitution score, you die."