[RPG] Can a Ranger learn spells outside the Ranger spell list

Extra Spell is specifically addressed in the FAQ (p. 40):

Can you take spells from spell lists other than your own with the Extra Spell feat (CAr 79)?

The Extra Spell feat allows you to choose a new spell, but it does not remove the restrictions of how you would normally pick your spells—so they must be picked from your own spell list.

This is the general rule -- you have a class ability that lets you cast spells from a particular class list only. For instance, the wizard has the following ability:

Spells: A wizard casts arcane spells which are drawn from the sorcerer/ wizard spell list.

For something to give you spells not on your class list, it has to explicitly call this out as an exception to the more general rule. The Master Specialist ability is worded almost identically to the wizard's regular spell book entry, so it clearly does not allow this:

When you reach 2nd level, you can add one spell of your chosen school to your spellbook. The spell can be of any level that you can cast, and it is in addition to the normal spells gained when increasing your level.

If it isn't on your class list, how would you even determine if it was a level that you can cast?

From the SRD (emphasis mine):

Although the alchemist doesn’t actually cast spells, he does have a formulae list that determines what extracts he can create
...
An extract is “cast” by drinking it, as if imbibing a potion—the effects of an extract exactly duplicate the spell upon which its formula is based
...
An alchemist can also add formulae to his book just like a wizard adds spells to his spellbook, using the same costs and time requirements. An alchemist can study a wizard’s spellbook to learn any formula that is equivalent to a spell the spellbook contains. A wizard, however, cannot learn spells from a formula book.

Alchemists cannot learn spells, they learn formulae, that are based on actual spells, but are not spells. Thus, if a wizard’s spellbook contains a spell that is the equivalent of a existing formula, you can study the spellbook to add that formula to your own formula book (essentially recreating the formula from the spell). However, the wizard cannot do the opposite.

Also, as a side comment, since alchemist extracts work like potions that must be ingested, makes sense that most formulae mimic spells that are either of personal range, buffs or healing, due that method of application. Attack and debuff spells could not be properly applied with that method (just imagine the consecuences of pouring a fireball down your throat), so it would not make sense that the alchemist could learn any wizard spell.