Taking the last questions first:
Breaking faith is a particularly serious sin involving a betrayal of a relationship or covenant. It is not simply another way of saying "they sinned." In the case of breaking faith, the problem is not just that a commandment has been transgressed but that a relationship between parties (whether between humans or between humans and God) has been violated.
Is this an unpardonable sin? No. This is evident from the OP's example of 1 Sam. 14. Men of the army ate meat wit blood in it. Leviticus 7:27 says "Every person who eats any blood shall be cut off from the people." Yet even though Saul declared they had broken faith, the soldiers in 1 Sam. 14 were not cut off. In the case of Exodus 21:8, the OP's ellipses (...) have created a false impression. The broken faith was not created by the daughter's father but by the Israelite man that her father sold her to. Her master was not supposed to sell her to a foreigner. Here, the broken faith is between the master and his slave-woman. It is up to her whether she ever forgives him.
Is there redemption after breaking faith? Yes. When the faith is broken between human parties, the offended party may forgive. In the case where being cut off from the people is the punishment this could be irrevocable (although the in incident in 1 Sam. mentioned in the OP proves the exception). When it was between Judah and God (Mal. 2), God did forgive:
They shall be mine, says the Lord of hosts,
my own special possession, on the day when I take action. And I will have compassion on them,
as a man has compassion on his son who serves him. (3:7)
The Case of Moses
Moses' case in Dt. 32 is different from the others mainly because the broken faith resulted from a direct command from God: to speak to the Rock rather than to strike it.
The Israelites, the whole community, arrived in the wilderness of
Zin... It was
here that Miriam died...Since the
community had no water, they held an assembly against Moses and
Aaron...The Lord said to Moses: 8 Take the staff and assemble the
community... and in their presence command
the rock to yield its waters... 10 Then Moses and Aaron gathered the
assembly in front of the rock, where he said to them, “Just listen,
you rebels! Are we to produce water for you out of this rock?” 11
Then, raising his hand, Moses struck the rock twice.
The people were in despair. Miriam had just died and now there was no water for them to drink. Moses was to renew the people's hope, provide water for them, and lead them to focus on the LORD as they prepared to march toward the Promised Land. Instead, Moses stuck the rock in anger at the people rather than with an attitude to lift up God's holiness. Because of this he lost his position as Israel's leader, and this role was transferred to Joshua. But this was not an unforgivable sin. God allowed Moses to see the promised land and spoke kindly to him just before he died.
The Lord then said to him, This is the land about which I promised on
oath to Abraham, Isaac, and Jacob, “I will give it to your
descendants.” I have let you see it with your own eyes, but you shall
not cross over... 8 The
Israelites wept for Moses in the plains of Moab for thirty days... 10
Since then no prophet has arisen in Israel like Moses, whom the Lord
knew face to face. (Dt. 34)