That looks like it should work.
No, since the rules say that an animal companion cannot serve as a familiar. I assume vice versa also applies.
This generally makes sense since the way the two level are completely different. Familiars level to have better minds, more magically relevant abilities, and to have better natural armor so they die less. Animal companions level to get better physical abilities, having better strength, dex, saves, skills and feats.
Improved familiars were made with the idea that they would level with familiar bonuses. The animal companion bonuses would make them level with far more focus on combat. Any combat abilities they had were already balanced, and this shift in rules would unbalance them. Plus, they often have many spell like abilities that are beyond what an animal could possess, which would make them more powerful than their similarly leveled animal companion counterparts.
If you want a more powerful animal companion, there are lists of more powerful animals you can choose from. This is without burning a feat.
Lemeres, Max stated he wanted both an Animal Companion and Familiar, not one serving as the other.
The Feat line will work, as Sir Gavvin stated...
that looks like it would work, unless youre talking about getting eldritch heritage - sylvan.
since under normal circumstances you cannot take sylvan sorcerer with eldritch heritage, because it is an archetype of fey bloodline, and the feat does not say anything about taking archetypes.
if youre talking about actually being a sylvan sorcerer with boon companion to get an animal companion, then taking eldritch heritage - arcane in order to get a familiar too, this is exactly what my pfs character did, in order to have both a lion AC (equal to his level)and a Lyrakie (Azata) improved familiar(at his level -2)
add a robe of arcane heritage and it works really well.
Ah sorry, coming right off the other thread about a hippogriff. I probably should sign off for the day. Not reading deeply enough anymore.