To my mind, the overriding rules here are these:
Alternate Form
The creature retains the type and subtype of its original form.
Undead Type
You cannot have an undead that has a Constitution score, so since Alternate Form has you retain your type, you cannot gain a Constitution score. I believe this is “more specific” than the general rule that you gain the target creature’s physical ability scores when using Alternate Form.
You could argue the opposite way, however, that Alternate Form is a more specific case than the general rule that undead do not have a Constitution score. But note that this results in a living (has a Constitution score) undead (retains that type), which to me is a good enough reason to side the other way.
As for using Charisma in place of Constitution, this is a common feature for undead, but not a universal one. In some places, that privilege requires a feat (e.g. Undead Meldshaping in Magic of Incarnum). Depending on your build, I might want to tax you for it; Cha-to-everything is a fairly potent strategy as it is, and undead is a desirable type anyway. Getting to use Charisma for yet more things, and avoiding the “weakness” of the undead type’s lack of Constitution, might be problematic. But if you weren’t already pursuing a Cha-to-everything build, I’d probably give it freely.
Yes it is more or less appropriate challenge, though it should be something like "boss"/"mini-boss".
As TheDarkWanderer pointed out Challenge Rating and average party level shouldn't necessarily match, so your party should probably be ok with a creature like that. After all CR system doesn't describe challenge really accurately, as it depends on multitude of different things like pre-scouting and builds.
You may still want to adjust this dragon for it to suit your needs more, but here is estimated 3.5e statblock based on information you've given:
Size/Type: Gargantuan Dragon (Fire)
Hit Dice: 22d12 +132 (275 hp) x3
Initiative: +0
Speed: 40 ft. (8 squares), fly 100 (clumsy)
Armor Class: 40 (-4 size, +44 natural [decreses slightly in later forms]), touch 6, flat-footed 40
Base Attack/Grapple: +22/+45
Attack: Byte +29 melee (4d6+11)
Full Attack: Byte +29 melee (4d6+11) and 2 claws +27 melee (2d8+5) and 2 wings +27 melee (2d6+5) and tail slap +27 melee (2d8+16)
Space/Reach: 20 ft./15 ft. (20 ft. with byte and tail)
Special Attacks: Crush, Tail Sweep, Lava Bomb, Earthquake Stomp, Shed Embers, Lava Vomit
Special Qualities: Darkvision 60 ft., Low-light vision, Dragon traits, Vulnerability to Cold, Immunity to Fire, DR 10/magic, SR 26, Paragon Fortitude, Paragon Fury, Blazing Form, Hardening Skin
Saves: Fort +19, Ref +13, Will +16
Abilities: Str 32, Dex 10, Con 22, Int 15, Wis 16, Cha 18
Skills: whatever
Feats: Multiattack, Power Attack, Improved Bull Rush, Awesome Blow (and 4 more feats of DM’s choice)
Challenge Rating: ~18
Crush (Ex) (4d6+16) DC 32;
Tail Sweep (Ex) (2d6+16) DC 32
Read
this about dragon specials. Note, while it is generally suggested to base these attacks on Con, I personally suggest to base them (as well as Earthquake Stomp) on Str instead, as they are basically area melee attacks.
Earthquake Stomp (Ex) (~2d6+16) DC 32
It is hard to convert this into 3.5 safely, since 3.5 is much less cartoon-styled, so just stomp would hardly be capable of causing Sonic (or what alternative is appropriate for Thunder?) damage. You may want to completely rework it.
Blazing Form (Ex) (~ 3d6)
Lava Bomb (Su) (~ 7d10) DC 27; Shed Embers (Su) (~ 9d10) DC 27; Lava Vomit (Su) (~ 12d10) DC 27
These are based on appropriate Breath Weapons of similar dragons.
I’ve added Fire subtype here, making Vulnerability to Cold and Immunity to Fire constant. You may of course reverse this, but it is how 3.5 generally deals with such cases, I believe.
Damage and Reach are now set as appropriate for gargantuan dragons. I added longer reach for the tail as it seems to have longest reach in the source. Gargantuan dragons usually also have Wing attacks (as well as Crush and Tail Sweep specs). Feel free to remove them if needed.
Bear in mind that this creature will became MUCH stronger when it will lose two of it’s pools. So it isn’t CR 18 from the start, but maybe somewhere close at it’s third pool.
Best Answer
Whatever resistances and immunities you decide it should have
This is a topic of disagreement inside Paizo's development team (and the community). There are those who are in favor of stripping the subtype immunities, and others who are against and defend that a creature should keep immunities from their subtype, and we have seen published creatures that attempt defend both sides, but none actually does.
One side defends that if a creature becomes a skeleton, it also loses the defensive abilities gained by the subtype (Immune to Fire damage for the fire subtype), while still being a creature of that subtype whenever it matters (like spells). For both subtypes at topic here (fire and cold), this interpretation makes little sense as that is all that the subtypes do (grant immunities and vulnerabilities), but for other subtypes it makes sense, like a white dragon becoming a burning skeleton, its a creature made out of flamming bones, why should it be immune to cold? The template immunities and vulnerabilities should take precedence over the (now lost) subtype.
While the other defends that the immunity gained by the subtype is not a defensive ability and is not lost, or that the type (and subtype) takes precedence over the vulnerabilities of the template. I personally disagree with the reason behind this logic, but it's the one that makes most sense when you consider the example from before (burning skeleton white dragon).
There is one published adventure that has an example of immunities stacking, on the City of Golden Death Module, where we are presented with Tar-Baphon's Dragon (SRD reference without the flavor). He was a Young Gold Dragon (Immune to Fire, Vulnerable to Cold) that was killed and returned as a Skeleton (Immune to Cold). The final creature is immune both to cold and fire damage and is the dragon on the cover of the module.
However, he is labeled as an "unique dragon" (as opposed to being listed as a dragon with the skeleton template) since it didn't become a mindless skeleton and retained many of it's special abilities, including spell-like abilities and the breath weapon. As such, not a completely valid example for this, but this is the closest thing published by Paizo.
There are cases of creatures that lost an immunity once they got a template, like the Zombified Storm Giant (SRD reference) from Carrion Crown #3: Broken Moon. But here, the immunities are granted by the creature, and not her subtype, which is exactly what the template says and thus it was lost.
But why would an immunity granted from a type, or subtype, which are nothing more than design shortcuts to a list of abilities that are common to different creatures (and unnecessary copy+pasting), be different from an immunity granted by the creature? In my experience, when they have to publish a creature that would cause problems like this, they make up a new creature and call it a day. Rarely we see creatures with templates that will simply point out to a bestiary book, and when they do, those are simple templates (like the advanced template) that shouldn't take much preparation from the GM to apply on the base creature. From a designer perspective, it is much better to create a new creature if you will already have to write full a statblock for them and avoid being inconsistent with the rules.
There is one published template that attempts to address both subtypes, the shadowfire creature from the Emerald Spire Superdungeon. The template specifically replaces the vulnerabilities the base creature had and add immunity to both cold and fire damage, as it becomes a creature of blackish fire. The creature gains both the fire and elemental subtype if they did not have them already (the example in the book are fire elementals).
Let's not even begin to talk about when a published book completely ignore the rules and create something new for the rule of cool, like the Lycanthrope Ghouls from Classic Horrors Revisited, which also adds both Fire and Frost Giant ghouls with the relevant subtypes and immunities from each.
In the end, you must see for yourself which is best for your creature and nothing in the rules forbids you to make a red dragon skeleton that immune to fire and cold, followed by another that is immune to cold and vulnerable to fire, and a third one that is immune to fire and vulnerable to cold. You could even create one that is immune to all energy types and still be a valid creature under the rules. You might want to adjust the CR by +1 though (seriously).