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Does the Alchemical Child get ALL the special qualities of the base creature? For example, does a Alchemical Child with "mind flayer" as the base creature retain all the mind flayer abilities?

Yes, the template in VRA specifically says "The Alchemical child retains all of [the] special attacks of the base creature (except class abilities...)" and "The Alchemical child retains all the special qualities of the base creature (except class abilities...)" (page 72)

So an alchemical child Mind Flayer would get the Mind blast, psionics, SR, telepathy, etc.. of a real Mind Flayer.

Go, Alchemy!

That's what I thought. Now if only the PrC was not such a lemon.

Here is a modification for the Alchemical Philosopher‎ Prestige Class.

At every odd level, the Alchemical Philosopher‎ gains one addtional caster level to which you belonged before adding the prestige class level, but not new spells per day or spells known. At every even level gain new spells per day and an increase in caster level (and spells known, if applicable) as if you had also gained a level in the spellcasting class to which you belonged before adding the prestige class level.

Now the Alchemical Philosopher is a potential choice for a PC.