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:

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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

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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.

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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.

Don't use CR

I don't think CR is going to solve your problems.

It would be great if you could plug in all the info into a calculator and pull out a number which will tell you how challenging the fight will be. And to be fair, there are a lot of very good CR calculators around.

However, the problem I have with them is that CR isn't very good from the start. CR is a rough approximation, but even if you calculated the CR perfectly, you still need to examine the situation more closely.

Asymmetrical Balance

One of the big problems you are going to have, is that NPCs are not PCs. PCs have incredible damage, but not much HP. Your wizard is the same, they have very little survivability, but a lot of damage. That's not the way NPCs should be built.

Take a quick look at your wizard; 30hp + False Life (lvl 3 slot: 2.5 + 4 + 10 = 16.5) = 47ish hp, 14AC. That's not a lot. Many level 3 classes will be dealing 1/3 to 1/2 that much damage on average. 14AC isn't a challenge for level 3 martial classes to hit either. A character could 1 hit that wizard with a luck roll and a crit.

And you have 3 lvl 3 PCs beating on this wizard, every turn. It's likely the wizard will be down before their initiative comes up, heck it's likely that one player won't even get a turn.

Difficult single enemies are easy to beat

Any time a monster is solo, it's vastly easier to beat. Lower level PCs can beat it down with their action economy. There's not much way around this, that's why stronger monsters have legendary actions.

So, what to do instead?

Firstly, don't use PC levels for an NPC. Pick the spells and features you want, and attach it to an existing monster of the right CR.

Secondly, make sure there are always minions in the fight. 1v3 isn't fair. 5v3 isn't fair either, but it's a lot more fun if the players win when the odds are against them! Even if they are only CR 1/4 skeletons, being outnumbered helps with the action economy, and it's fun.

Thirdly, play test. Yes I know, it's a pain, it would be great if you can just plug it all into a formula, right? But play testing will give you a much better understanding. There is no way to accurately predict how your players will react, but using their PCs to test is the closest you can get. It's not as hard as you may think. If you have their character sheets it's pretty straight forward.

Or, like I do, throw all that away

I used to play test, to make sure everything went smoothly. But now I don't. It doesn't matter if things do not go smoothly, actually I personally prefer it. I'm not saying you should throw vastly stronger things at the players, but a little too strong is fine.

If players run in and steamroll your wizard? So what. There are other enemies in the game, don't sweat it.

If players struggle with the wizard, losing a lot of hp and resources? Again, so what. It's up to them to manage their resources, and handle fights and pacing.

I find this works a lot better. The story emerges from the players actions instead of from my head. This makes them happier since their actions are the story, and me happier because I don't have to worry making a good story for the players. This is part of an overall player-driven philosophy to running games. I'm not going to try turn you away from narrative games in one swoop, but if you think about facilitating your players actions instead of dictating them, then you may find unbalanced encounters to be less of a problem.