Yes, they would stack as described.
I couldn't find this spell in the wonderful SRD (which is still a wonderful resource and can answer a lot of rules questions for you), so @JonathanHobbs and @BESW dug up a link to the spell in Complete Arcane. The text is as follows:
This abjuration grants a creature and its equipment complete protection against damage from one of the five energy types—acid, cold, electricity, fire, or sonic.
Energy immunity absorbs only damage, so the recipient could still suffer side effects such as drowning in acid, being deafened by a sonic attack, or becoming immobilized in ice.
Note: Energy immunity overlaps protection from energy and resist energy.
So long as energy immunity is in effect, the other spells absorb no damage.
Emphasis mine, of course.
Repeat castings do in fact stack, creating a near-total immunity to energy damage (this spell notably does not protect you from force damage, positive energy damage or negative energy damage). On the one hand, this is fairly powerful. On the other hand, 6th and 7th level spellcasting isn't a joke and it does burn up spell slots.
The stacking rules in 3.5 have to do with two things and two things only unless there's a specific exception in the wording of a spell or ability - bonus type stacking, and same source stacking. Bonus types - such as dodge bonuses, inherent bonuses, or insight bonuses - differentiate the sources of a bonus to a roll. With some small amount of exception, two bonuses of the same type (such as two enhancement bonuses) do not stack if you attempt to apply them to the same value. Likewise, two bonuses from sources with the same name do not stack, nor do two abilities or spells with the same name stack - if, and only if, they're trying to add or modify the same values or abilities. Though multiple instances of Energy Immunity do in fact have the same name, they're not trying to modify the same values or abilities - each one gives immunity to a different kind of energy. Thus, they stack.
But you can't have a wand of it.
The player can't buy a wand of energy immunity for the simple reason that it's a 6th level spell for divine casters and a 7th level spell for arcane ones, both well above the limit on wands (to wit, they can only contain spells of 4th level or lower).
Paralysis immunity does not imply stun immunity.
Being paralyzed is not an increased form of being stunned. Their sources and actual effects are completely different:
- is frozen in place.
- cannot move at all, its Str and Dex are, effectively, 0.
- is helpless
- has generally been the victim of a paralytic poison or spell.
- is unable to take actions, but can still take nonactions (like a 5-foot step).
- loses its Dex bonus to AC (if any) plus suffers a −2 penalty on Armor Class (and a foe's combat maneuvers that use its CMB gain a +4 bonus).
- drops any held equipment.
- has usually been the victim of powerful or tactical blows, such as to the head.
Paralyzed means you are completely frozen in place, whereas stunned means it's like getting hit by a boxer's right cross to the chin — you're so close to being knocked out, you can't properly defend yourself — that you're basically just stumbling around.
Best Answer
Yes
Because Immunity provides automatic success on relevant resistance checks (Hero's Handbook page 113), and because Suffocation (Hero's Handbook page 186) and Starvation and Thirst (Hero's Handbook page 186) are resisted with Fortitude checks, immunity to Fortitude does protect the character from suffocation and starvation and thirst.
and Maybe
Sleep is a different problem. There are no rules about resisting the biological need for sleep, aside from the Rank 1 Immunity. Immunity (Fortitude) would make the character immune to sleep effects resisted by Fortitude resistance checks, such as the sample Sleep power (Hero's Handbook page 129), but not to sleep effects resisted by Will resistance checks.
So, whether or not the character needs to sleep depends upon GM adjudication, specifically about what checks are required to resist falling asleep outside of power effects. Arguments can be made for both Fortitude and Will checks, and ultimately you'll have to choose the answer that is the most fun for your table.
Personally, I don't see why his not sleeping is a problem. Being awake doesn't make you alert, as proven by real life bored and inattentive guards or phone-distracted pedestrians walking into traffic.