[RPG] Is a creature immune to a spell’s damage type immune to the spell’s other effects

To my understanding, reducing an ability score to 0 causes a condition that can't be avoided by natural resistances called "helpless".

All of this is mentioned in the basics section of the Hypertext d20 srd:

Ability Score Loss

Some attacks reduce the opponent’s score in one or more abilities. This loss can be temporary (ability damage) or permanent (ability drain).

While any loss is debilitating, losing all points in an ability score can be devastating.

• Strength 0 means that the character cannot move at all. He lies helpless on the ground.
• Dexterity 0 means that the character cannot move at all. He stands motionless, rigid, and helpless.
• Constitution 0 means that the character is dead.
• Intelligence 0 means that the character cannot think and is unconscious in a coma-like stupor, helpless.
• Wisdom 0 means that the character is withdrawn into a deep sleep filled with nightmares, helpless.
• Charisma 0 means that the character is withdrawn into a catatonic, coma-like stupor, helpless.

If you're immune to paralysis you can't be affected by things like ghoul touch, but things like hold person affect you (since hold person is a mind-affecting compulsion). Immunity to paralysis prevents you from being physically immobilized through spell effects.

The golems in your example are immune to hold person because it's a mind affecting effect and they have no intelligence score. The unicorn has an immunity to compulsion effects (which hold person falls under as well), which further distinguishes the difference between paralysis and hold.

Loss of ability score causes gain of helpless so even if you were immune to paralysis, you'd still be rendered immobilized when reduced to 0 dex regardless.

What an interesting question.

Under RAW, it would not heal. Spell Secrets is pretty specific that only the damage type is substituted, and furthermore, at least for the wording under Vampiric Touch the healing specifically comes from necrotic damage dealt.

Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt. Until the spell ends, you can make the attack again on each of your turns as an action.

Technically there was no necrotic damage dealt here. And that makes sense. Why would fire damage heal the caster like siphoned off necrotic energies.

That said, RAI, it would not be the end of the world to extend the healing to this power.

NOTE: Unearthed Arcana is playtesting material, and may not be balanced, worded well, or workable.