For the meaning in Mark:
Jesus' questions about the numbers of loaves and baskets in Mark 8:19–20, which involve symbolically significant numbers, suggest that we should consider further the meaning of the wilderness feedings. Jesus also speaks of "the yeast of the Pharisees and the yeast of Herod" (v. 15), so we should consider how this might be involved.
These issues can be illuminated by considering where our passage (8:14–21) is located in Mark's Gospel to understand its literary context. Scholars have come to recognize that Mark has arranged the episodes in his Gospel in order to convey added theological meaning. For example, consider the central section of Mark from 8:22–10:52 (which immediately follows our passage). Many scholars recognize that 8:22–10:52, in which Jesus tries repeatedly, without any apparent success, to get his disciples to understand that he as Messiah must suffer and die (and be raised from the dead after three days) (8:31; 9:31; 10:32–34), is framed by the two healings of blind men in 8:22–26 and 10:46–52. The first of these healings is distinctive in that Jesus is at first unsuccessful (8:24). Whatever literal meaning the healing stories have, they are given an additional symbolic meaning by where Mark places them, namely that they convey the seriousness of the disciples' "spiritual blindness" which Jesus struggles to "heal". Our passage (8:14–21), in which Jesus also asks whether the disciples "have eyes and fail to see" (v. 18), leads directly into this central section.
8:14–21 serves as the climax of the entire section of Mark 4:35–8:21. Werner Kelber (Mark's Story of Jesus, 1979) proposed that Mark uses the several boat journeys in this section to help organize the literary structure, such that some episodes take place in "Jewish" territory and others in "Gentile" territory. (There are many potential complications here. See Ched Myers, Binding the Strong Man, pp. 187–89.) In this approach, the feeding of the five thousand (6:32–44) takes place in Jewish territory, and the feeding of the four thousand (8:1–10) takes place in Gentile territory. The numbers of loaves and baskets helps confirm this: In the first, Jewish, feeding, there are five loaves (calling to mind the five books of Torah) and twelve baskets of broken pieces (recalling the twelve tribes of Israel). In the second, Gentile, feeding (which follows immediately after events in the Gentile territories of Tyre in 7:24–30 and the Decapolis in 7:31–37), there are seven loaves and seven baskets of broken pieces. Seven is widely used in the Bible as a number symbolic of completeness or fullness, which in this context may suggest that Jesus' ministry is only truly complete when Gentiles are included in its blessing.
Now in 8:14–21, Jesus and his disciples are in the boat in between the Jewish and Gentile sides of the lake, which on a literary level holds symbolic significance. Jesus warns the disciples about "the yeast of the Pharisees and the yeast of Herod" (v. 15). These were two different groups that took different approaches to the relationship between Jews and Gentiles. The Pharisees emphasized adherence to Jewish dietary practices in such as way that they resulted in an exclusive meal practice; Jews were not to eat with Gentiles (cf. 7:1–23). The Pharisees emphasized such practices in part in order to preserve Jewish cultural identity in the face of pressure to assimilate to the dominant Greco-Roman culture of the Roman empire, but the result was a stance of isolationism and antagonism. Herod, on the other hand -- here referring to Herod Antipas -- was a half-Jewish client ruler who collaborated with the Roman empire. He built the city of Tiberias as a fully Greek city with a Greek constitution, and divorced his wife in violation of Jewish law (David A. deSilva, An Introduction to the New Testament, p. 66). He can be seen as representing assimilation and integration with the dominant Greco-Roman culture, and the erosion of Jewish cultural identity and religious traditions (Ched Myers, Binding the Strong Man, p. 224). Jesus' movement offered a third way, one which opposed Pharisaic isolationism and antagonism towards their Roman "enemies" (Matt 5:44) and instead called Israel to return to the best of her ancestral traditions and her calling to be the light of the world (Matt 5:14–16), a model of a people living in faithful obedience to God, to be a blessing to all nations (Gen 12:3). (Much more is said on this in books such as Marcus Borg's Conflict, Holiness & Politics in the Teachings of Jesus and N.T. Wright's Jesus and the Victory of God).
The disciples have one loaf in the boat. Jesus' focus on the number of loaves in Mark 8:19–20 hints that we should ask whether this one loaf has a symbolic significance as well. The Greek word commonly translated "bread" throughout this passage is the same word as for "loaf" (artos), only in the plural, and so could be translated as "loaves". This opens up the possibility that the contrast is between the single loaf they have and loaves plural. Following Kelber, it seems we are meant to understand that one loaf is enough. Not separate table fellowship, where Jews have their loaves and Gentiles have theirs (this was an issue the early church struggled with, as can be seen in Gal 2:11–14). No. One loaf, one table, one Jew-and-Gentile people of God together in unity. That answers your first question: The disciples do not understand the symbolic meaning of the one loaf.
The disciples do not understand, and Jesus asks, "Why are you talking about not having loaves (plural)?" (Mark 8:17). Jesus' questions are not about the disciples forgetting that he has miraculous power to feed a large crowd. If that were the case, one would expect Jesus to emphasize the number of people fed ("When you had only five loaves, how many people were you able to feed?"). Instead the questions place the emphasis on the number of loaves and the number of baskets, numbers that have symbolic significance along the Jewish/Gentile dimension. Jesus' rebuke of the disciples is also especially harsh, characterizing them in 8:17–18 as having "hardened hearts" (recalling Pharaoh in the Exodus story), and eyes that do not see and ears that do not hear -- a quotation from Jeremiah 5:21, where Jeremiah warns the nation of Judah of coming judgment for their sins. The language is used to compare people to idols, which have eyes that cannot see and ears that cannot hear. The gravity of Jesus' rebuke suggests that the issue in question is incredibly serious and gets to the heart of Jesus' message. One may ask whether trust in Jesus' miraculous abilities is a sufficiently fundamental issue. If it were the issue, then Jesus could satisfy the Pharisees' demand for a sign in 8:11–12 so that they would be able to trust his ability to do miracles. But he doesn't, because it is the orientation of their hearts, and their understanding of the character of God and of what sort of people Israel's God was calling Israel to be that were the more fundamental issues. Both the Pharisees and the disciples needed to understand God's will for his people to be a blessing to all peoples without putting up barriers of separation.
Regarding your second question, we would run into the issue of how much of 8:14–21 is historical and how much is created for literary effect. This could be a whole other topic. None of the above requires denying the historicity of the passage, though I consider it more plausible to see the passage as an entirely literary creation of Mark. Mark's intent would not be to deceive, but rather to faithfully express Jesus' orientation towards Jews and Gentiles and to convey how Jesus' mission and message should be worked out in the meal practice of the early church. It is tricky to explain the psychology that would lead to the disciples' response in Mark 8:16, but I can see it being part of a depiction of the disciples as exaggeratedly dull and stupid created as a literary foil for Jesus' dialogue.
For the meaning in Matthew:
Most scholars believe the Gospel of Matthew used Mark as a literary source, which I assume here. Matt 16:6 replaces "Herod" with "Sadducees". Sadducees were by and large high-priestly elites who collaborated with Roman rule, so a similar point to that made above for "the yeast of Herod" could be made about the "yeast of the Sadducees." Matt 13:53–16:12 for the most part preserves Mark's order from Mark 6:1–8:21 (though Mark 6:6b–13 is moved earlier), while material from Mark 4:35–5:43 is moved earlier to Matt 8:23–34; 9:18–26 with a large amount of intervening material placed in Matt 9:27–13:52. The result is the separation of boat journeys in the narrative. Mention of the Decapolis is removed in Matt 15:29 = Mark 7:31, and the location "along the Sea of Galilee" is ambiguous. So Matthew preserves some features that support the above interpretation of Mark, while losing others, so it is unclear whether Matthew intends to make all of the same points. Matthew adds 16:12, "Then they understood that he had not told them to be on guard against the yeast in bread, but against the teaching of the Pharisees and Sadducees" (NRSV), which at least could fit with the above interpretation for Mark.