This...this looks really good! Nothign to OP, all well written, and I think it would be fun to play this engineer. Well done. Mind if I download the Docs as source material for when I put an engineer in my homebrew game?
A while ago, based on the "designing classes" section in the ACG, I made a list of questions that I think everyone, before proposing a class, should ask themself:
1) Can my idea really not somehow be done with an existing class, e.g. with a new archetype?
2) Is my idea seperate enough from every single existing class?
3) Does my idea contain a brand new primary class feature*?
3b) (for hybrid classes) Is this new class feature either a blend of different parent class features or a new spin to a common parent class feature?
4) Is my idea strong enough to support multiple playstyles?
5) Is my idea suitable for actual play in an average game?
6) Bonus question Does the class allow character shaping choices**?
*) "Primary features are a signature of the class. These abilities advance in power and utility as the class progresses through its levels, and improvements to these features are often one of the things players look forward to most as they play a member of that class. (...) Note that while primary features tend to be isolated to just one class, secondary features might appear in multiple classes." ACG pg. 243f
Note that apart from #6, all these question stem from the guidelines in layed down in the "designing classes" section of the ACG. #6 does not, and is indeed broken by multiple Paizo classes, but is indeed necessary to make a good class, as you can see if you read the spoiler right below. Also note that most of the many complains about the Shifter stem from the class breaking these guidelines left, right and center.
Such character shaping choices come in three forms:
1) Daily: Mostly spell preparation, Shaman's Wandering Spirit/Hexes, and the Medium's spirit.
2) On levelup: Spells known, rage powers, etc., doesn't have to be every level up
3) One time: Domains, bloodline etc., mostly done at first level
I don't count feats, skills, and equipment because it should be obvious that options that literally every class can take have to be relatively weak (otherwise almost every character would take them, cf. Leadership for what happens when this rule is broken). I also don't count choices that don't affect playstyle and only grant minor numeric bonuses, such as a Fighter's weapon training.
Archetypes are technically one time choices as well, if these are included depends on what we want to compare.
Naturally, the more choices you can make, the more you can (in general) shape your character. Also, the more often you can make choices, the more flexibility the character can have. Daily choices don't add power over on levelup choices, but they add a lot of flexibility.
The following classes are generally accepted to be the weakest ones in Pathfinder: Fighter, Brawler, Rogue, Cavalier, Samurai, Gunslinger, Swashbuckler, Monk.
Apart from the Rogue ***, you'll notice that none of these classes have a daily or on levelup choice ****. Cavalier and Samurai have a one time choice at first level, while the others don't get to make any character shaping choices at all. It's also noteworthy that there are no classes lacking daily or on-levelup choices that are generally considered good.
Now, choices don't automatically contain strong options (few rogue talents are better than feats), some fixed class features are fairly powerful as well (like rage), and there are options that offer choices to make on the fly, like wildshape or a Summoner's SLA (not character shaping by definition, but can be very powerful). But if you look at both power level and flexibility, there's almost no getting around having class features that allow character shaping choices fairly often.
***) Whoever thought that a pure martial with medium BAB, no accuracy increasing abilities, d8 HD, and the worst possible saves a PC class can have was a good idea?
****) Fighter got on levelup choices with AAT and AWT, while Monk got on levelup choices with UnMonk's Ki Powers and Style Strikes.
Your class is better made than most other I see, as #s 4 and 6 are covered. Seriously, that's rare - most people focus on one very specific concept and try to make an entire class out of that. #5 should be fine as well (which is normal, the question is mostly there to prevent stuff like pure skillmonkey classes with no combat potential). It's #s 1-3 that I'm not satisfied with. #1: There is already an Alchemist with firearms, the Gun CHemist, and it works very well. This severely lesens the need and neiche for your class. #2: Education feels like a modified Vigilante Specialization, and is responsible for making the class feel less cohorent. Most of the class features are taken from other classes.
What the class is really lacking at is #3. I don't really see a signature class feature. The Inventions, are nice in themself but not really enough to carry the class (again same thign Vigilante has).
Your main problem is actually that you're starting with a class that should not exist in the first place. Gunslinger is basically a Fighter archetype that trades half the bonus feats for the atrociously designed deed system (it's lacking character shaping choices), plus a few initial bonus feats. With some work done, your Engineer class could as a replacement for the Gunslinger (i.e.the class the Gunslinger should have been), but I don't see how it could be called a hybrid class. Because crappy as it is, the deed system is basically the Gunslinger's signature ability - the whole firearm stuff is a few feats, nothing more (apart from the "you can start with one" stuff that only lasts like two levels).