Question 1: Was the tabernacle (then later the Temple) the ONLY place under all circumstances that sacrifices could be made? According to the sacrificial laws in Leviticus, the limitation of sacrifices seems to be to the tabernacle/temple. For example, Lev 1:3 says in part, “He shall bring it to the entrance of the tent of meeting.” A similar statement is made with regard to most of the other sacrifices specified in Leviticus. Likewise, Deuteronomy 12:4-14 limits the place of the sacrifices in a similar fashion. It does appear, however, that at certain times and on special occasions, sacrifice would be carried out elsewhere. So Elijah offers a sacrifice in 1 Kings 18, rebuilding an altar of the Lord that had been torn down. Likewise, David built an altar and had sacrifices offered on it at a place away from the tabernacle (2 Sam 24). But the regular sacrifices seem to have been limited to the tabernacle/temple.
Subsidiary question A. What about when a person is cured of a skin disease, or a woman is cleansed from an unusual flow of blood? Yes, that person would have to undertake the onerous task of visiting the sanctuary and offering sacrifice. The requirement for the woman to offer two turtledoves or two pigeons (Lev 15:29) does not refer to her regular menstrual uncleanness, but to an unusual flow, like the woman in Matt 9:18-26, and parallels.
Subsidiary Question B. How were the Levites supported, if they did not receive portions of the sacrifices? They had fields and livestock in their cities. See Num 35:1-5. In addition, Deuteronomy consistently refers to the need to support the Levite, as well as the fatherless and the widow. The Levites were responsible to teach the law among the people of God, and the people (implicitly) were to pay them for that work.
Question 2: How was it possible for the Israelites to attend the three annual festivals? Deut 16:16 specifies that it was the males who were to present themselves three times a year. We know from Luke 2 that by the first century, many entire families went. First, God promised to keep the land safe during the annual festivals (Ex 34:24). It is true that there would be massive amounts of sacrifice offered at those times. But remember that even by the time of the building of the temple, the priesthood was a sizable caste in Israel. It also seems likely that additional altars would be set up to deal with the crowds. It is also unlikely that everyone brought sacrifice three times a year. An interesting consideration of the offerings spelled out in Leviticus 1-5 is that there is no requirement given as to how often these sacrifices were to be made. They were at the discretion of the offerer.
Subsidiary Question A. Did Israel actually keep the feasts? Some did. My reading of 1 Sam 1:3 is that Elkanah and his family went up three times a year. I realize most translations say something like “from year to year,” but it is literally “from days to days.” This I understand to refer to the appointed pilgrimage festivals. There are six separate accounts of keeping of Passover in the Old Testament, and the language used implies that the festival was celebrated more often than that, but that these were very special for one reason or another.
Subsidiary Question B. How did Jerusalem (or Shiloh, at an earlier period) handle such a massive influx of people? I would say the same way that they handled it in the first century (Luke 2 and Acts 2 both refer to masses of people being in the city for the festival). For a week or so, people lived in crowded, busy conditions. For those who have had the experience, it might be likened to the attendance at a NASCAR race. Surrounding the racetrack are hundreds upon hundreds of RVs and campers, parked nose to tail. Depending on which race track is in view, the attendance at a NASCAR race can range from sixty to two hundred thousand people, and those are all housed within a fairly limited radius. Granted, it is a larger radius than the crowds in ancient Israel would have occupied, but we Americans like our space, even when we attend huge events. On the other hand, there were perhaps half a million at Woodstock (yes, I’m dating myself) all within a very small radius. In short, I don’t think it was that difficult for Jerusalem to handle the crowds that showed for the festivals