First of all, don't take this reply in the wrong way,

I'm merely retorting here... I can't just sit still... lower your sarissas
Xenophon, you wrote:
It is hard to know where to begin, considering that it is already apparent from the above alone that your knowledge of matters military is not very deep. I fear that, as Paralus has pointed out of others, your views of Alexander's abilities are coloured by admiration, rather like Lane-Fox's views - by the way, as Paralus has hinted, some of his views on matters military are a little peculiar to say the least.
OK, my knowledge doesn't run that deep, I prostrate myself before you, then, Xenophon almighty... Paralus didn't mention anything about my admiration of Alexander - he spoke of Lane Fox. So Fox's stock hasn't risen that much in your eyes, then? Well, he was only personal advisor to Stone on the movie set, and he only holds an Oxford research fellowship..
Robin Lane Fox on Alexander vs Rome:
"Alex was not in the least worried by Rome ...if they sent him an embassy to Babylon they were probably worried by him....I think the phalanx under Alex ,with the cavalry above all ,might have beaten the Romans ...Alex wd not have been caught on terrain as bad as at Pydna ...and he was SO inventive ,with the Sh Bearers and Cavalry at their peak...King Perseus was not in his class and even so the Romans had problems..."
You said:
Military fact 1: Ancient armies were generally unable to exceed approximately 50,000 men for logistic reasons. This is all the more so in a mountainous country like Greece or Italy. Nobody in ancient times could, or did, bring more than that many invaders to Italy and keep them supplied in a hostile country. As Livy points out, Alexander's vast Eastern manpower was useless.
Check out Xerxes... what about the roman army at Cannae... countless other examples... Now, if Rome, could refill and recuperate manpower and losses, then why couldn't Alexander? Rome was stubborn, yes? but believe me, Alexander was ten times worse. He'd never, ever have given up, and in his own words, "the more difficult something is, the more important it is to accomplish it".
Magnesia? That was not a major army... sources are discrepant as ever on the figures.
If alexander had gone after the Romans as the were in his lifetime he would have most likely crushed them, mainly because their armies were still hoplite based being very similar to what Alexander was used to fighting in greece and so he would know how to effectively counter them.
Also there would have been plenty of neighbouring peoples that would have happily joined Alexander against the Romans such as the Samintes and Latins.
Also, I think a lot of people are making the mistake of veiwing the Romans of Alexanders time in light of their acheivements later in history, there was nothing special about the Romans in this time, they didn't use innovative new tactics, they weren't anymore better at fighting than other peoples, their population wasn't particularly bigger than others, they weren't anymore diplomatically cunning. Rome was still literally fighting for her life at the age of Alexander, internal strife and external threats...
What they were was a smallish regional power among others jostling for power, three years before Alexanders death they became involved in the Second Samnite war, it took 22 years for them bring it to an end and even then the Samnites were not completely defeated. If it took them that long to defeat a group of (admittedly tenacious) mountain tribes how would you expect them to do the same against a newly arisen superpower at the peak of its strength with thousands of harderned veterans lead by generals experienced in combating numerous battle tactics including those very similar to the ones the Romans used at the time.
At best they would have fought a few battles before conceeding defeat and become a client state, at worst if they were stubborn and resisted to the very end Alexander might have made a example of them and razed Rome to the ground like he did with Tyre and Thebes.
Believe me, Alexander would have found a way... he always did...
Also, Alexander knew of the situation with Rome and Carthage but wasn't in the least worried... it was way down on the to-do list...
Fortune is nothing more than a case of preparation meets opportunity....