The important thing to understand about Xerxes' logistics when he began his march west in 481 BCE is that this was not a massive venture into the unknown. Not only had the Persians and Greeks been in near-constant conflict for almost 20 years, but every inch of land the Persian army had to cross was already conquered right up to the border of Macedon and Thessaly in northern Greece. That's not to say there weren't complications - I'll get to those - but it's important to understand the Persian tool kit, especially in regard to your second question. We don't have access to detailed Persian logistical plans or military records, but we do have Herodotus' Histories and a series of other less detailed Greco-Roman accounts. The first half of Histories book 7 is all about the preparation, organization, and movement of Xerxes' army.
This is not just an emphatic yes from me, but from Herodotus. Herodotus only rarely has any direct insight to events beyond the Greek speaking world, but he was relatively knowledgeable about events that occurred in or immediately nearby the entire Greek sphere, including the Greek cities of Anatolia in Persian territory. He seems to indicate that the Persian forces marshaled in two location in Anatolia before crossing into Europe.
One contingent, the larger of the two which traveled with Xerxes in 481, started in Capadoccia according to Herodotus. The other gathered in Cilicia, a common rendezvous point for Persian forces. Herodotus lays out the journey of these two forces separately, though he doesn't make a clear distinction between them in his storytelling. Reading through that journey is a bit like playing connect the dots with the rivers, streams, and major cities in between. This pattern of tracing the movement of the Persian army by naming the bodies of water they passed continues after Herodotus transitions to their movement through Thrace.
Herodotus does identify cities that they passed by like Thebe Hypoplakia, which were not located on a river. However, given that these were cities they must have had some water source, be it lakes, canals, springs, or wells. Very clearly, access to fresh water was part of the Persian logistical plan. These routes were well traveled, both by merchants and travelers and by armies stretching back to the Bronze Age who followed similar paths to the Persians in 480.
No account of the Persian water supply on the way to Greece is complete without talking about the River Skamander, which Herodotus says was drunk dry by the massive Persian force. This has been extrapolated further by authors both modern and ancient to an obviously apocryphal story of the Persians "drinking whole rivers dry," as an example of Herodotus exaggerating the Persian numbers. In reality, Herodotus' story of the Skamander is not too absurd, even accounting for the fact that it was probably the smaller western army that refilled their water skins there.
Calling the Skamander a river is being very generous. It is a narrow, silty stream, and at several points in history, it did not even reach the sea during a dry season. The idea that a military planner, not perfectly familiar with the region may have planned to stop there and found it insufficient for tens of thousands of men is not outside the realm of possibility. It just has to be noted that even Herodotus does not suggest that this was a regular occurrence.
Supplies were prepared in advance for the armies arrival. No merchant, or even a city, could just supply the Persian army out of the blue. A relatively average sized military force was a burden, but even accounting for Classical authors' exaggerations, Xerxes' army in 480 may have been the largest military force ever assembled, certainly the largest ever deployed in the eastern Mediterranean. 300,000 people isn't outside the realm of possibility and 80-100,000 are frequent estimates. This was not a group you could just go shopping for.
This was also not a surprise in any way. According to Herodotus, the Persian empire spent almost a decade planning for the invasion of Greece. Darius was supposedly already prepared when he died in 486, only for those preparations to be squandered on the rebellion of Egypt and Babylon after Xerxes came to power. Whether that's true, or Herodotus' own inference is impossible to say. After that, Xerxes was said to have spent four years preparing for his own invasion. The Asiatic Greeks would have been well aware of this, given that the army had to pass through their cities, and a large portion of the navy and the famous pontoon bridge was built in their shipyards.
The advanced warning was a necessity. Even with preparations, the Persian advance to Greece was not lacking in logistical challenges. Herodotus puts these concerns in the mouth of Xerxes uncle, Artabanos, though in reality he just uses Artabanos as a character to convey logistical concerns.
For the sea, I believe, has no harbors anywhere that are large enough to receive your fleet and guarantee the safety of your ships should a storm arise. And you require not just one harbor, but many of them, located all along the entire coast of your expedition’s route. Since there are no ample harbors, you must realize that fortune will now rule over the affairs of men instead of men ruling over their own fortunes. Having thus explained one of two adversaries, I shall now describe the other. The land has also become your adversary, in that if no one comes forth to oppose you, the land itself will become more and more hostile to you the farther you advance and are lured into going ever farther, since human beings never have their fill of success. (Histories 7.49.3-5)
This is partially Herodotus foreshadowing some of the logistical problems faced by the Persian military after entering Greece. However, it also hints at some of the Persian planning on the way there. Herodotus goes on to describe how the Persian fleet shadowed the army along the coast until they reached Chalkidike (at which point the coastal geography necessitated separating). This is not the first time Herodotus mentions this practice. The same tactic was employed over a shorter, more hostile distance when the Persian's first conquered Egypt. The fleet was able to act a limited supply depot while the army was on the move. Once in hostile territory, ships could also cross the Aegean sea quickly to ferry supplies to the army from friendly territory.
From the Persian administrative perspective, military service, logistical support, and labor were all requirements of Persian subjects. It was comparable to the tax burden. Each city and region were assessed for what they could provide and then they had to provide that or face punishment. As I said, there were years of forewarning, but how each territory prepared for the army's arrival was up to them. It obviously necessitated an increased tax burden. Whether those taxes were in-kind (collecting foodstuffs directly) or in coin (collecting currency and then buying provisions for the army) was largely dependent on local economics. Many smaller cities would have needed to implement a combination of both, supplementing their own agricultural produce with imports to meet Persian demands.
The Greco-Thracian cities east of Chalkidike understandably saw the worst effects of the Persian logistical demands. These were relative small cities that had to host the army and the navy at the same time. Herodotus reports that hosting Xerxes led to functional famine or near-bankruptcy in several cities, specifically naming Thasos and Abdera. These cities and Macedon, may have been the only regions outside of Greece to host the full Persian military all at once.
I mentioned two mustering points in Anatolia above, but the eastern army that started its march in Capadoccia also broke for winter quarters in the winter of 481-480 and dispersed across western Anatolia. Herodotus says that it took seven days for the whole army to cross the bridges over the Hellespont. Once again, this is something that some suggest as an example of Herodotus exaggerating the size of the army, but from a logistical perspective it would make sense to divide the army into separate sections and march them into Europe in separate waves.
Herodotus explicitly states that a similar tactic was employed for exactly these reasons later on. When the army reached Chalkidike and had to separate from the fleet, they were split into three separate columns, each with their own route, so as not to impose too large a force on any one Thracian settlement at a time. These three columns rejoined the fleet at Therme (modern Thessaloniki). King Alexander I of Macedon then had to host the full force while the Persians made plans and prepared to march into Greece for the first time.
Supplies didn't immediately run out once they crossed the line. The Kings and cities of Thessaly in northern Greece had already invited the Persians and prepared to host them as well, but Herodotus still implies that Persian intelligence up to that point was limited and had to be reassessed, with some aspects of the route through Thessaly being re-planned. While that was happening, Greek forces from Athens, Sparta, and their allies were occupying the Tempe Pass, the primary route through the mountainous border between Macedon and Thessaly. Alexander I sent word to this Greek army that they were hopelessly outmatched and Xerxes was now planning to take a different pass, circumventing their force altogether.
Alexander I is complicated figure with complicated motivations, but one popular theory among historians is that Alexander framed his advice as goodwill toward the Greeks, but desperately needed to get the Persian army moving out of his own territory because they placed too much burden on Macedonian resources. The Greeks withdrew and the Persians advanced.