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When a wizard gains a level, his familiar's effective hit dice change:
Hit Dice: For the purpose of effects related to number of Hit Dice, use the master's character level or the familiar's normal HD total, whichever is higher.
Are the familiar's feats an "effect related to number of Hit Dice" or does this statement apply only to the effect of certain spells that affect a certain HD range? For example, assume a wizard just reached 7th level and has a small air elemental as a familiar (nominally a 2HD familiar). The familiar is treated as having 7HD for "effects related to number of Hit Dice", so would the familiar get feats at 3 and 6 HD as if it were an advanced air elemental?
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Nope. When it says 'effects related to Hit Dice' it means things like whether or not the familiar would be put to sleep by a Sleep spell, it's hit dice for how Color Spray interacts with it, etc. It never gains new feats, ability points, etc. This was covered in the 3.5 FAQ and has not changed with the Pathfinder RPG. Feats are not an 'effect related to Hit Dice', they are something you gain when you actually gain Hit Dice. A familiar's real Hit Dice do not increase.