Really hard to say if casting off HP is balanced or not, since the current game doesn't have anything like that I could compare it with. The best you can do it tell your players that this is a playtest and that if things get out of hand you might need to adjust mechanics. (Or do extensive playtesting beforehand).
As to scaling the powers of the gems, I would really encourage you to have different levels of the elemental gems emulate existing spells. Say the first level Fire gem does Burning Hands, then Scorching Ray, then Fireball, etc.
This might not be what you're looking for, but I have tried doing something similar once. I ran a game using d20 Modern rules but set in the Final Fantasy 7 world, and we used a Materia system. Materia gained as much experience as the character gained from an encounter, and when it gained the same amount of XP a sorcerer would need to cast the next level of spell, then it learned that spell, and any character could later equip it.
For example, a Fire materia started off with 0 XP and knowing Burning Hands, since a first level Sorcerer with 0 XP would be able to cast it. To be able to level the Fire materia to it's second tier spell (Scorching Ray), it required having the Fire materia equipped for as many encounters as it took a character to earn 6000 xp, because that's how many experience points it would take for a Sorcerer to become level 4 (using the Fast track for advancement in PF) and be able to cast 2nd-level spells like Burning hands. In order to cast it's third tier spell, Fireball, it needed to be equipped for as many encounters as it took a character to earn 15,000 xp, because that's when Sorcerers are high enough level to cast 3rd-level spells like Fireball. In the end, it was a pretty elegant system since if you wanted to be able to cast Fireball as early as possible, you had a Fire materia equipped since level 1, but if later in your character's life you wanted to start using a brand new 0-xp Fire materia, 15,000 xp might not be such a huge investment (being less XP than necessary to go from 8th to 9th level), while still rewarding the early-equippers by giving them first available access to the spell. For higher level spells (like Meteor Swarm) from rare materia (like the Comet materia) that the party wouldn't be able to find at an early level and couldn't possibly gain the XP to learn their spells, we had armor and weapon properties that could double or even triple XP gain for equipped materia, but these were worth +3 and +5 price adjustments, respectively.
As far as casting, since we were trying to emulate Final Fantasy, we went with an MP system, and gave every class a basic MP progression (like psionic classes have a PP progression), and every spell had a casting cost of (Spell Level x 2) - 1 (1st level spells cost 1, 2nd cost 3, 3rd cost 5, etc.). I'm not sure if a similar costing scheme would work for casting from HP instead of MP, but I would try to follow a similar formula.
As far as the no magic except through the gods thing goes, how picky are the gods when it comes to giving out magic? For instance if there's a god/ess of magic her followers could become the equivalent of wizards without too much of a change other than, possibly, the schools of magic being more akin to the various domains. In fact the line between a cleric and wizard could be eliminated entirely.
As far as the stones go, the health cost does effectively limit their usefulness per day unless everyone wants to take a different turn using them. I'd recommend treating what the stone does as an equivalent spell and work it out from there. For instance:
0-level abilities are constantly useful just like cantrips and orisons. 0-level abilities would replicate the appropriate 0-level cantrip or orison effect or an equivalent effect. Using a 0-level ability does not cause any damage to health.
1st-level abilities can be used an x number of times per day by the same person per level before incurring 1d6 damage to health:
once a day at first level without penalty
twice a day at second and third level without penalty
three times a day at fourth through sixth level without penalty
four times a day from seventh level on without penalty
2nd-level abilities can be used an x number of times per day by the same person per level before incurring 2d6 damage to health:
once a day at third level without penalty
twice a day at fourth and fifth level without penalty
three times a day at sixth through eighth level without penalty
four times a day from ninth level on without penalty
3rd-level abilities can be used an x number of times per day by the same person per level before incurring 3d6 damage to health:
once a day at fifth level without penalty
twice a day at sixth and seventh level without penalty
three times a day at eighth through tenth level without penalty
four times a day from eleventh level on without penalty
4th-level abilities can be used an x number of times per day by the same person per level before incurring 4d6 damage to health:
once a day at seventh level without penalty
twice a day at eighth and ninth level without penalty
three times a day at tenth through twelfth level without penalty
four times a day from thirteenth level on without penalty
5th-level abilities can be used an x number of times per day by the same person per level before incurring 5d6 damage to health:
once a day at ninth level without penalty
twice a day at tenth and eleventh level without penalty
three times a day at twelfth through fourteenth level without penalty
four times a day from fifteenth level on without penalty
6th-level abilities can be used an x number of times per day by the same person per level before incurring 6d6 damage to health:
once a day at eleventh level without penalty
twice a day at twelfth and thirteenth level without penalty
three times a day at fourteenth through sixteenth level without penalty
four times a day from seventeenth level on without penalty
7th-level abilities can be used an x number of times per day by the same person per level before incurring 7d6 damage to health:
once a day at thirteenth level without penalty
twice a day at fourteenth and fifteenth level without penalty
three times a day at sixteenth through eighteenth level without penalty
four times a day from nineteenth level on without penalty
8th-level abilities can be used an x number of times per day by the same person per level before incurring 8d6 damage to health:
once a day at fifteenth level without penalty
twice a day at sixteenth and seventeenth level without penalty
three times a day at eighteenth and nineteenth level without penalty
four times a day from twentieth level without penalty
9th-level abilities can be used an x number of times per day by the same person per level before incurring 9d6 damage to health:
once a day at seventeenth level without penalty
twice a day at eighteenth level without penalty
three times a day at nineteenth level without penalty
four times a day from twentieth level without penalty
I was thinking only those that are the highest in their respective religions would be granted any magical abilities at all.
As far as allowing some use to them with no penalties I have mixed feelings about this idea. It would allow me to keep the lower level spells more useful as leveling happened, but I would like to scale down the damage as you level up as apposed to eliminating it entirely.
An alternative route that I thought of is essentially adding mana to the game, and if it runs out it starts to do damage to your hp, but I'm not sure how well that would work either.
Okay, that makes sense.
Well, I may have been misunderstanding the nature of the stones, but one other possibility could be to use mana and the damage I suggested - that is, you 'pay' to use the stone in terms of mana at some set rate that limits the number of times you can use a given stone or a certain power from a given stone in a day (the stone, itself, could still be used, it just gets more dangerous to do so). A person's mana increases by level so a person could use the stone to do something more times a day or a more powerful ability without worrying about it harming the character.
For instance a fire stone could:
0-level causes 1d3 fire damage/imitate spark without costing mana
1-level causes 1d4/level fire damage (max 5d4) or touch delivers 1d6/level fire damage (max 5d6) or imitates dancing lantern or similar
Using it would cost 3 mana per use. Once all mana is used it causes 1d6 points of damage per use.
2-level causes 1d6/level fire damage, or touch delivers 2d6/level damage or causes a pyrotechnic-like effect. Using it would cost 9 mana per use. Once all mana is used it causes 2d6 points of damage per use.
3-level causes 1d6 fire damage per level, 20-ft. radius or deals 1d6/level fire damage. Using it would cost 15 mana per use. Once all mana is use it causes 3d6 points of damage per use.
And so on. Basically, the stones could imitate certain spells in terms of damage or effects. The 0-level effects could be used all the time just as cantrips/orisons are. When imitating a higher level spell it costs an increasing amount of mana to use. This cost could be mitigated by the level of the user. For instance a 1st level user using a 1st level power only expends 3 mana but using a 2nd level power expends 9 mana and so on - whatever rate you deem best.
A third level user using a 2nd level power would only expend 3 mana, but would expend 9 mana to use a 3rd level power and so on.
Does this make sense?