The Advancing Companions section in the Pathfinder System Reference Document seems to indicate that the answer is yes on all counts:
Another issue is who gets to control the companion's advancement. Animal companions, eidolons, and cohorts all advance much like PCs, making choices about feats, skills, special abilities, and (in the case of cohorts) class levels. Whoever controls the companion's actions also makes decisions about its advancement, but there is more of a shared role between you and the GM for some types of companions.
Cohort: A cohort is generally considered a player-controlled companion, and therefore you get to decide how the cohort advances. The GM might step in if you make choices that are inappropriate for the cohort, use the cohort as a mechanism for pushing the boundaries of the game rules, or treat the cohort unfairly.
(emphasis mine) and from Aspects of Control:
Sentient Companions: a sentient companion (a creature that can understand language and has an Intelligence score of at least 3) is considered your ally and obeys your suggestions and orders to the best of its ability. It won't necessarily blindly follow a suicidal order, but it has your interests at heart and does what it can to keep you alive. Paladin bonded mounts, familiars, and cohorts fall into this category, and are usually player-controlled companions.
And in Monster Advancement.
Adding Racial Hit Dice: Adding racial Hit Dice to a monster is a similar process to building a monster from scratch. As additional Hit Dice are added, other abilities increase in power as well. Additional Hit Dice usually results in better attack bonuses, saves, hit points, and skills, as well as more feats. It can also include additional spellcasting capability and other powers.
All but the last of these passages can be found in Ultimate Campaign. The last passage is part of the Bestiary, on page 295.
Since what spells a faerie dragon knows are a decision it makes as it advances in racial HD, and since you, not the GM, control such advancement, and, in fact, determine all aspects of your familiar with only minor oversight (as shown above), you can certainly swap out a faerie dragon's spells known as you generate it, just like you can its skill points, feats, and all other decision-based aspects of its character.
As for item usage, the dragon casts spells "like a sorcerer", so for items which benefit from or require sorcerer spell ability (like a wand of Fireball or a Staff of Meteor Swarm or, like you mention, Pages of Spell Knowledge) the dragon qualifies as a sorcerer. However, it is not a sorcerer and so items that rely on it being one (class requirement items) or possessing other class powers (Robe of Arcane Heritage) would not function.
You are right that the spellcasting does not increase as you (the master) level up, but if the familiar were a wild faerie dragon it would increase with additional racial Hit Dice, as per the normal rules for advancing monsters with spellcasting ability.