[RPG] Learning new languages

Speaking, No. Understanding, Maybe.

The few Familiars that can automatically speak, do so "as a supernatural ability."

From PFSRD:

Familiar Basics

Skills: [...] Regardless of a familiar's total skill modifiers, some skills may remain beyond the familiar's ability to use.

and further down that page:

Intelligent Animals

Increasing an animal's Intelligence to 3 or higher means it is smart enough to understand a language. However, unless an awaken spell is used, the animal doesn't automatically and instantly learn a language, any more than a human child does. The animal must be taught a language, usually over the course of months, giving it the understanding of the meaning of words and sentences beyond its trained responses to commands like "attack" and "heel."

Even if the animal is taught to understand a language, it probably lacks the anatomy to actually speak (unless awaken is used). For example, dogs, elephants, and even gorillas lack the proper physiology to speak humanoid languages, though they can use their limited "vocabulary" of sounds to articulate concepts, especially if working with a person who learns what the sounds mean.

So, to expand my answer a little... No they can't speak it, unless the animal has the right anatomy to produce speech. They can be taught to understand languages, though.

(You could argue that the gaining of a point of Linguistics reflects the months of learning a language, so that being Awakened is not a requirement.)

Familiars automatically meet the Intelligence requirement:

Familiar Ability Descriptions

All familiars have special abilities (or impart abilities to their masters) depending on the master's combined level in classes that grant familiars, as shown on the table below. The abilities are cumulative.

Master Class Level Natural Armor Adj. Intelligence 1st–2nd +1 6 ...

I have always read

You gain the selected language as a bonus language,

as meaning that you add the language to your list of known languages when you create your character (as a bonus language), not that you add the language to the list of bonus languages you can choose from to learn with a high intelligence modifier. The reason I believe this is that it says you "gain the language as a bonus language," not "add it to your available bonus language options" as other similar features do.

This is no different in my view from gaining a bonus language from a high intelligence modifier.

You apply your character's Intelligence modifier to:

• The number of bonus languages your character knows at the start of the game.

I interpret this as meaning that it is a bonus language because it is not a language you have learned through a rank in linguistics or from your racial features -- that is, it is a bonus on top of your standard known languages. Essentially, you have a list of languages to choose from, and when you gain one from high intelligence or a class features, it becomes a bonus language. They are bonus languages because they do not require ranks in linguistics to learn them (because a linguistics rank allows you to learn any language). When you become an oracle you gain that language as a bonus.

The text that follows,

At 5th level, pick an additional language to speak in combat and add it to your list of known languages,

indicates to me that the language added at 5th level is in addition to the bonus language gained at level 1.

Unfortunately, there is no real explanation for why the game writers used two completely different phrasings to mean the same thing, if you accept the premise in this answer as true, and, absent any developer or writer commentary on why such choices were made, I doubt we can make a determination on that.