How did a Legion get new recruits if it was stationed in a border province and the requirement for a Legionary was that he was a Roman citizen (before Caracalla)? Were there recruiting offices in Italia?
The legions did not have permanent stations in the provinces (mostly) until the reign of Augustus. Before that, they rotated out and were attached to individual commanders more than places. In the more distant places (like Spain, Macedonia, and Asia Minor), things were a little more complicated, but still held to the same principle. As new Roman magistrates came to "take over," they frequently brought with them fresh levies to replace those that had been lost or had been discharged or whatever. In Summer of 86 BCE, Valerius Flaccus left from Italy with an army to deal with Mithridates' invasions in the East. Awkwardly, Sulla was already in the East with another Roman army, fighting the same war. When he left, he had Rome's blessing, but after he arrived the government of Rome was replaced and so was the "official" commander. Both Sulla and Flaccus continued to fight, one in Greece and one in Asia Minor. Had things been more friendly, Rome might have sent Flaccus to assume control of the Sullan army (as they had tried to do previously, in Italy before Sulla departed). In either case, the armies were recruited in Italy, not in the theater of war. This was of course for the infantry; things are different for the cavalry, who were by the mid-1st BCE almost always allied contingents instead of Romans.
Recruitment was in the hands of the individual commander. For instance, we find Caesar recruiting legions in Cisalpine/Transalpine Gaul in 59/58 BCE for his conflict against the Helvetii. Pompey raised a force of his father's old veterans in Picenum to join Sulla in 83, when the latter returned to Italy and marched on Rome. Caesar, technically, had a mandate from the SPQR to raise troops to conduct Roman business; Pompey, meanwhile, just had ambition and initiative. After 88 BCE, all the former Italian allies became Romans and therefore eligible for recruitment into the legions (hence Caesar in the north). Before that, the Italian "allies" had provided parallel contingents of infantry (that looked and fought like legions, but got less booty).