I would like to preface this question by saying that I am in no way asking if VMC counts towards level prerequisites for feats, that is already known as a resounding no.
Now: Are abilities gained through VMC taken into account when taking feats? (Such as Extra Arcane Pool with VMC magus 3rd level ability Arcane Pool.)
The only times this is called out as a definite no no is in the case of VMC oracle and VMC witch; both of which call out they never qualify for Extra Revelation/Extra Hex.
Thoughts?
Do you have the Arcane Pool class feature? Yes. VMC Magus grants you the Magus's Arcane Pool class feature.
Do you have Rage or Bardic Performance? Yes. VMC Barbarian/Bard gives you those class features.
You qualify for Extra Arcane Pool because it only requires you have the Arcane Pool class feature... which you do, by name. Same with Extra Rage/Performance... and everything else that is called out as forbidden. If you have the class feature, you qualify for the Extra Whatever feat to go with it.
You can even take Extra Grit with your one Grit point from Amateur Gunslinger, so yeah, you can take Extra Arcane Pool with VMC Magus. Like you already pointed out, the ones where you cannot say that you cannot.
Are abilities gained through VMC taken into account when taking feats? (Such as Extra Arcane Pool with VMC magus 3rd level ability Arcane Pool.)
"A character who selects this option doesn’t gain feats at 3rd, 7th, 11th, 15th, and 19th levels, but instead gains class features from her secondary class" PU pg. 88
Everything gained from VMC is gained as a class feature, even though it's not gained from class levels.