My point is, with so much emphasis on the security of their technology, why would the Andalite military permit the a Blue Cube (that, we later on learn, can seemingly automatically charge ANY species with the morphing power by a mere touch) to be taken on the field. It shouldn't have left the Homeworld in the first place.
It does lead me to your first hypothesis, that of Elfangor quite simply having taken the Cube that would have been issued to him. BUT, it doesn't explain having no fail safes on the Andalites' part. Remember, Seerow's Kindness is judicial for them.
One reason could be because the Andalite Fleet was that; a fleet. It was meant to be a mobile home, home to thousands of andalites, and essentially a walking base. As a walking base, it was essentially the most protection they could have outside of having it on the main base on the homeworld.
Essentially, when the fleet journeyed to stop the Yeerks, I don't think any of them had any illusions as to how long the war was going to take. None of them was going to say 'a few years' and from the series, we've known that the entire war lasted more than half a century, with the pivotal battle being the last three years on Earth.
Since the war was expected to last long (what with the Yeerks considered a plague, and we all know how hard it is to stop an intergalactic plague), the Andalite Fleets would have probably been expected and built to be self sufficient. They would not have had to keep returning to the homeworld, be it for supplies, and/or upgraded military technology. (remember that the Escafil Device existed since the Hork Bajir war, but even then it was brand new; by then, upgrades in technology could have been vast, and if such technology was made only on the home world, the andalites would have basically been fighting with old technology. Essentially, they needed to keep the technology they had achieved on their mobile bases, either to further upgrade or explore the tech rather than having to return to the homeworld to do it every time).
lastly, we have to remember that the andalites take great pride in their dome ships. They never expected to be ambushed by the pool ship and subsequently, tthe blade ship. if the andalites had to take morphing technology out of their homeworld (with the reason being that it was impractical to return to the homeworld everytime they needed the cube for whatever reasons) it would have to be on the most safest place it could possibly be; ie. on a dome ship. Assigning one cube to each war prince would have simply made it so that there would be multiple people responsible for each cube; therefore shoulld the cubes ever need to be accounted for, the war princes need nearly be called up. Since each cube was entrusted to one war prince, no single person (save the Captain prince himself, maybe) would be able to compromise their entire stock of morphing technology. Also, since they wouldn't all be stored in the same place, a lucky thief or traitor wouldn't be able to send all the technology they had to the Yeerks.
Elfangor was a War Prince, but he was not leading the trip to Earth. That goes to Captain Nerefir, whom was the Captain Prince of the Dome Ship GalaxyTree. As for the photo, it would have been of Elfangors, his brother and their parents. The photo was never shown to be how old.
For your second hypothesis: I'm only partly with it. I think that is the problem with the having all-powerful-time-fiddling characters such as the Ellimist. Eg: I still can't buy the 'lethal wound' that incapacitated him to heal through morphing... though there have been some plausible hypothesis relating to the Ellimist being at work (which you can find here in this thread somewhere). But there again, we have the Ellimist doing the Deus Ex Machina guimmicky.
it wasn't the wound, it was exhaustion. Morphing requires focus, and Elfangor was too weak to even move into his ship and get a box. While it may not be a great reason, it was necessary for Elfangor to die, because his death was the primary motivation for the Andalites to keep fighting. Without his sacrifice, the animorphs would have just run away, pretended the truth never happened, and an alien didn't die in front of them. If they weren't shown how tough and dangerous their enemies could be, they would have been irresponsible with their power (which they only are very occasionally),.
David was a good example of an animorph who, without seeing the sacrifice of someone, and had lost everything he had (from his parents, his life, his home) and ended up hating the animorphs for dragging him into their fight.
Elfangor did have full awareness of what was to happen, but only after he met Tobias. He had brought the cube for reasons unknown (but which had no doubt been ensured by the Ellimist). he had met the five children, one of them his own son from a life long ago. It was only then, that he chose to broke the law and give those five children morphing powers, because it was he alone who knew what human children could do. That, and because he knew that his son would join with four others and his own brother, and that this union was of great significance to the ellimist. Having known that, he decided to entrust the animorphs with the morphing power.
It was also shown that Elfangor never intended to give the power to them. he had traveled to Earth, because he was defeated, dying and desperate enough t resort to the one weapon neither side could ever been allowed to possess; the Time Matrix. He failed, and he would have died, if not for the anirmorphs.