Ghaleon holds the sword in several sequences, actually. For starters, he BLATANTLY POINTS IT AT HIRO right before the fight starts in an FMV ("Now that you've failed in every possible way, blah blah blah HIRO!" is the scene I'm reffering too), and he's blatantly holding the sword in the fight against him. Think many of his attacks involve him using the sword in some manner (like I believe Meteor Shower actively shows him holding the sword up and it flashes, and I think his basic physical is a simple slash at close range with it, not surprisingly.)
Pretty ridiculous to say "That's not the same sword he gave Hiro!" really. Lets think about EBC Ghaleon for a second...
He WANTS Hiro to succeed. That fight was basically a test to see if Hiro had truly given up, and to see if he actually stood a chance against Zophar (if they couldn't beat Ghaleon, then its fruitless to go after Zophar given Zophar is a few levels above Ghaleon in power.) Furthermore, given how he was living, the best he COULD do is Help Hiro in the most hostile methods possible, given, you know, his life force was dependent on Zophar and if he suddenly did something that was clearly treacherous (like he does after the fight when he openly admits he was pushing for their success), he just fades away as we saw (hence the reason all he did for Hiro was hand him that super Sword, instead of outright helping him firsthand; he flat out couldn't.)
...but that's just getting into EBC plot specifics. Point is, there's no reason to assume that the Sword Ghaleon uses both in the cutscene AND when he fights Hiro is not the same sword he hands Hiro to defeat Zophar.
Regarding the Summoner thing...
We only see 3 living summoners, and Belgemine, yes. However, the game implies there are others, as they keep talking about how the Al Bhed is kidnapping summoners and stopping pilgrimages. Yes, when we finally get to where they are captive, we only see Isaaru and Donna (and Isaaru's Guardians), but I chalk that up to Square being lazy to create other characters who'd be summoners. The fact remains, the Al Bhed kidnappings were mentioned happening throughout the game, and they imply they were successful on these occasions (so its not just the few attempts or so they tried on Yuna throughout the game and failed.)
There's also former summoners too, like in the Calm Lands, we meet that one guy whose now an official of Yevon or something. He apparently was the summoner Wakka and Lulu were working for prior to Yuna, and like most summoners only got as far as the Calm Lands and gave up.
Given all this, and how characters like Dona have only one Guardian at a time, you'd think some of them would be relying heavily on Aeons for protection, and due to this, its logical to assume that there are moments when there are two Valefors being summoned at once. I can easily buy the theory of "the same Aeon can't be summoned if its already summoned in proximity" or some such...or perhaps its a simple case of "Aeons refuse to fight themselves!" so summoning Bahamut on Bahamut leaves a useless stalemate, thereby making the match pointless, so its "He who summons first gets full Aeon privlages!" or something.
(really, I personally just chalk it up to a game play excuse to keep the idea that you're actually summoning, and you can't have one guy in two places at the same time cause its awkward. But that's just me.)
Like Elfboy said, Dona's competitive and all, but she only really talks about how Yuna's pathetic in using so many guardians, and is more treating it like a race. She doesn't do any of this "I'd appreciate it if you stopped using MY Aeons, thus interrupting MY pilgrimage!" or some such.
Its a gray area in any event. But the only proof that you can't summon 2 of the same Aeon at the same time is a game play based one, which is shakey.
FF Games have always changed the plot of summons, before someone uses a different excuse. Look at the plot of FF6 Espers, FF8 Guardian Forces, FF4 Summons/Phantom Beasts/whatever they're calling them now, FF9 Eidolons and FF10 Aeons, and they're all completely different. Yes, you summon them, but how it works is different between games (FF9 Eidolons, for example, were contacted through the use of the Summoner's Horn IIRC (which...apparently still works even if the horn is removed ala Garnet. This could be Eiko botching facts though...)), and the plot behind them is also different. No, this doesn't serve much purpose in this debate, I'm just trying to kill any potential branch off arguments before they come out, as FF games are very much inconsistent about summons cause every world is different, etc. so the plot of them changes.
(I purposely left out FF3, FF5, and FF7 in that list above cause Summons are a pure gameplay device that are absolutely plotless, especially in FF7's case.)
The point is, you're adding rules that aren't explicitly stated. It comes down to the whole "You can't disprove it, therefore its right!" argument.
We aren't getting anywhere with this. I could argue something as simple as this, however, if you're so bent on "Yuna's Aeons cannot be summoned twice at the same time!"
Yuna, by the end of FFX, is the ONLY TRULY ACTIVE LIVING SUMMONER LEFT. Isaaru is stuck having to fill in the role of Maester cause he's apparently the best fit, given the turmoil Bevelle is in (or something along those lines), Seymour is dead, and Dona outright states she was thinking about giving up the Pilgrimage.
So...now Yuna's left being the only one with that power, if indeed those are the only summoners in the world (which could very easily not be the case.) Hey look, its suddenly unique!
You know what this reminds me of?
Ryu3 being the only Dragon with any sort of Power left by the end of BoF3 as far as we know. Yes, the game mentions Dragons that live underground, but as far as we know, they were all of Ryu's tribe and long since died and he's the only one left (Dauna Mines and such.) You can say there's more than meets the eye, but that just goes back to speculation based on "You can't disprove it!" and yeah, can of worms. Otherwise? Only Dragons left are Ryu, Teepo, and those in Dragnier.
In Dragnier, the only Dragon with power is Jono, holding the Infinity Gene, awaiting the arrival of Ryu.
Eventually, Jono and Teepo are dead, that leaves Ryu with the only one who can use these Genes!
Not seeing how that differs from an Aeon; its a similar (albeit not identical) concept. In fact, it falls back to the whole uniqueness thing:
Ryu wasn't the only one with the Infinity Gene; Jono CLEARLY used it in order to turn into Elder Dragon. He openly states he's holding onto the entire power of the Brood (and which is what the Infinity Gene is), so now Ryu can't go Kaiser Dragon in the DL, I suppose, since Jono used the main ingredient.
That argument is pretty ridiculous, in any event. Trying to justify Gameplay restrictions based off uniqueness of plot.