I'm glad to see you're putting alot of thought into what would suit you best and trying to learn more about what you're putting in your vehicle

You've asked some good questions, I'll try to answer them all, from the top:
What about a coax with a crossover?
Does that make the soundstage and such noticeably better than one without?
All coax's have a "crossover" of some type; even on cheaper coax's, you'll find an INLINE crossover. This means that the midrange driver will usually be full-range, but if you look at the positive speaker lead going to the tweeter on a coax, you'll find a little resistor that acts as a high pass filter for the tweet. It's usually a very cheap, shallow dB/octave crossover (meaning it's filtering effect is weak and will allow SOME midrange frequencies to through to the tweeter). What's important is that the set uses an OUTBOARD crossover, rather than INLINE. An outboard crossover uses both high-pass filters (for the tweet), and low AND high pass filters (for the mids). Some higher end outboard crossovers can include things like variable crossover points and slopes, subsonic filters (eliminating wandering frequencies outside the 20-20kHz range), and thermal overload protection to save your drivers from excess wattage or clipping. So YES, a coax with an outboard crossover will have a better sound than a coax with no outboard crossover. And YES it's soundstage will be better than a component set because the tweet is on the same axis as the mid driver. A MAJOR benefit of these Infinity speakers are the ability to pivot and aim your tweeter, as high frequencies are the most directional of all.
The kappas come with a crossover I understand, sending the sound two places instead of just one?
The kappa coax uses the crossover to split the signal into mid and high, but it's final destination is the same: the coax. You'll have to run two speaker leads from the crossover to the coax, one for the mid driver and one for the tweeter.
Now will it be that much of an improvement over just having the reference series in all four doors?
Oh yeah.
And furthermore, would it be beneficial (meaning, worth the money) to step up to a component system, like the infinity kappa 680.7cs for the front doors?, and then either of the two coaxials for the back.
If you don't mind the tweeter placement restrictions of the Explorer door panels, I do think you'd greatly enjoy the pleasure of separates up front. They are more aimable (<--is that a word?), can handle more power, and of course, look cooler

. If you DO put components up front, coaxials will be your best bet for the rear. Rear coaxials provide additional volume while keeping the tweeters are out of the way enough to not interfere with the soundstage at YOUR listening position (the only important position in the truck, as far as I'm concerned). Whatever series you decide to go with up front (kappa, reference, etc) its a good idea to put the same series in the back so the speaker build material and basic sound characteristics will be similar.
There is also an infinity reference series component system 6810cs, which I'm guessing is still better than coaxials, being that it is component, but just not as clear as the kappa components?.
The reference components will have a better separation and filtering than the coaxials and will sound much better, yes. As for the comparison between the reference and the kappas, it's like apples and oranges. I like oranges. You may like apples. The sound from each series will differ because of speaker characteristics and build materials. Expect the Reference to have softer sounding highs because of its silk-dome tweeters as opposed to the kappas metal tweeter. The kappas will have better separation and less coloration than the references due to the stiffer midbass cone and steeper crossover slopes (the 6807cs has a the best crossover of the aforementioned). Of the two series, statistically, the kappas are much better (higher wattage rating, higher sensitivity, wider freq. response, better crossovers) but some like a soft, mellow sound rather than a crisp, clean sound and for them the reference would be a better choice, especially at mid volume. I highly recommend finding a local dealer of Infinity speakers and listening to each series for yourself to determine which one suits your personal taste the best.
Hoping I Didn't Forget Anything,
~stu