Q1. Read Exodus 32:1-14. What had the people done that was so bad? How can a loving God be angry? Is God's sentence to destroy Israel and raise up a new nation through Moses justified?
I don't think they so much rebelled, as forgot. (If they had rebelled that would have had to be against something real and they no longer thought of God as real.)
Even though they had seen the power of their one God in the plagues in Egypt, deliverance from Egypt they stopped trusting and believing in him (who they could not see) just because the human leader was now (and for 40 days) out of sight. They don't know if Moses will ever return and they confused Moses with God and felt abandoned. Their prayer could have been "bring us a new leader" but instead they turned from God Himself.
God loves his nation and anger at their rejection is entirely justified. If he didn't love them, he wouldn't have been angry.
The sentence isn't "justified" as, since there is no covenant yet by which to measure justice, there can't be justice.
But his sentence is fair, and common sense. His promise was to the nation, not to this particular generation.