Animal Companions

[Light Knight]

While a druids animal companions levels, does it gain more feats/skills?

 

[StreamOfTheSky]

Yes.

 

[Sekhmet]

Animal Companions have been the source of much errata.
I highly recommend Rules of the Game: Animals (Part Four)
A quite quote for you that addresses your specific issue;

The animal companion gains extra Hit Dice as noted in the table on page 36 of the Player's Handbook. The companion gains the full benefit from increased Hit Dice, including increased base attack, base saves, skill points, and feats. The animal companion, however, does not increase in size (any more than you do when adding Hit Dice for your class levels).

Bolded for emphasis.

 

[StreamOfTheSky]

That leaves out the question of raising an ability score every 4th level. But that's just part of raising HD in the monster advancement section, so it seems pretty clear to me. The only hard rule to apply that isn't spelled out well enough that I'd recommend you make as a DM is: You cannot raise the animal's Int above 2 (going from 1 to 2 is fine), as it is then no longer an animal and cannot be your companion anymore.

 

[Sekhmet]

There are a few feats that give your Animal Companion higher Int, or allow you to take Magical Beasts or others, but without these feats, StreamOfTheSky is correct.