Alexander the Great by Philip Freeman is a good read. It's directed at laymen and thus is less dry than most strictly academic works. I can only answer for what Freeman's work says, so if he was wrong, I hope someone can post a correction.

1. Yes, according to the sources we have he fought in all the major engagements of his army during his famous campaign eastward.

2. It wasn't common, for example Darius (leader of Persian Empire) did not fight with his troops. However among smaller, more tribal states such as the Scythians, the leader would fight with the rest of the troops. According to Freeman Alexander's participation was often crucial to morale. Alexander's army won battles in which they were outnumbered by absurd margins (such as at Gaugamela), as well as won offensive sieges by force on cities that seemed basically unconquerable (Tyre and Gaza). Freeman says that Alexanders gusto and personal participation was what kept morale from breaking when his army stood up against immensely larger forces or extremely impressive/legendary fortresses. Overall though it's certain that it was seen as an act worthy of respect, honor, and greatness. The sources (likely) exaggerate some of the stories in an attempt to embellish Alexander, so it was certainly seen as a positive thing to have bravery and battle prowess in a leader, as opposed to someone like Darius who watched comfortably from the rear. There is something innate in people, especially soldiers, to want to follow the leader charging the enemy king instead of the helpless leader running away.

3. He was trained extensively in horsemanship and fighting, as well as general education, from a young age by his father Philip. His father had access to excellent teachers from the kingdom he had built around Macedon during his life and Alexander is said to have had a host of tutors, Aristotle among them. It's reasonable to assume that he would have been an excellent fighter, and surviving sources of course wouldn't say otherwise.

4. Don't know more about this than the average person.

5. Besides Freeman there are countless academic works. However I would recommend just reading A Life of Alexander by Plutarch, a prominent ancient source, or this compilation of ancient sources.

Was it expected of generals of the time? What did other commanders and soldiers think of him throwing himself into the gray time and time again? What was he trying to prove by doing it?

Alexander was the product of a tradition - both Greek and Macedonian - of leading warriors by example. In Greek city-states, this was the only recourse for citizens elected to the generalship to prove that they were worthy of the position; among the Macedonians, rather, it fit into older notions of leisure-class competitive display, in which the man who claimed the right to lead had to prove that he had what it took to deserve the leadership. The outcome was the same. All generals were obliged to lead from the front. It was the best way to inspire the men and to get them to do what they had to do. Indeed, Alexander's alleged obsession with Achilles would have encouraged him to behave in the fashion of Homeric heroes, who were constantly trying to outdo one another in acts of bravery and feats of arms in order to justify and secure their high social status.

Even though the Greeks were aware that the loss of a general could be fatal for an army, even military thinkers still recommended that generals lead from the front, aware that a general who was perceived as cowardly would not be able to get anything done. Greek warriors' preference for the "soldier's general", who shared in the hardships of the men and led by example, resulted in a staggering casualty rate for Greek commanders. It's often been remarked that Alexander's survival despite mutliple wounds received in close combat was little short of miraculous. Only in the later Hellenistic period do we see generals (starting with Pyrrhos of Epiros) taking a more managerial approach to battle command.

Since his time, have generals attempted to emulate his style of 'heroic' leadership by leading from the front?

As noted above, his style wasn't new; it was the norm for all generals in the Greek world, from elected Boiotians to Spartan kings. However, if anything, Alexander's example made the trend worse. Since the men who filled the power vaccuum after his death derived their status primarily from their military prowess, and the chief way to prove one's military credentials was to emulate the greatest commander ever - Alexander - a lot of the so-called diadochoi (Successors) shared the same reckless habit of leading from the front.

Plutarch discusses the matter in detail in the introduction to his Life of Pelopidas, a fourth-century Greek general who died in battle:

For if, as Iphikrates analyzed the matter, the light-armed troops are like the hands, the cavalry like the feet, the hoplites like chest and cuirass, and the general like the head, then he, in taking undue risks and being over bold, would seem to neglect not himself, but everyone, inasmuch as their safety depends on him, and their destruction too.

Therefore Kallikratidas, although otherwise he was a great man, did not make a good answer to the seer who begged him to be careful, since the sacrificial omens foretold his death; ‘Sparta,’ said he, ‘does not depend upon one man.’ For when fighting, or sailing, or marching under orders, Kallikratidas was ‘one man’; but as general, he comprised in himself the strength and power of all, so that he was not ‘one man,’ when such numbers perished with him.

Better was the speech of old Antigonos as he was about to fight a sea-fight off Andros, and someone told him that the enemy's ships were far more numerous than his: ‘But what of myself,’ said he, ‘how many ships will you count me?’ implying that the worth of the commander is a great thing, as it is in fact, when allied with experience and valour, and his first duty is to save the one who saves everything else.

Therefore Timotheos was right when Chares was once showing the Athenians some wounds he had received, and his shield pierced by a spear, in saying: ‘But I, how greatly ashamed I was, at the siege of Samos, because a catapult bolt fell near me; I thought I was behaving more like an impetuous youth than like a general in command of so large a force.’

For where the whole issue is greatly furthered by the general's exposing himself to danger, there he must employ hand and body unsparingly, ignoring those who say that a good general should die, if not of old age, at least in old age; but where the advantage to be derived from his success is small, and the whole cause perishes with him if he fails, no one demands that a general should risk his life in fighting like a common soldier.

One of the most interesting works on Greek command is E.L. Wheeler's 'The General as Hoplite', in V.D. Hanson (ed.) Hoplites: The Classical Greek Battle Experience (1991).

Edit: added Plutarch quoting me