[RPG] Is an Ooze a living creature

Nope!

Shrink Item is specifically designed for an object, for which creatures do not qualify. You're wanting either Reduce Person or Reduce Creature.

Or Reduce Animal, as the case might be. http://archive.wizards.com/default.asp?x=dnd/lists/spells&tablefilter=reduce

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• Wisdom 0 means that the character is withdrawn into a deep sleep filled with nightmares, helpless.
• Charisma 0 means that the character is withdrawn into a catatonic, coma-like stupor, helpless.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.