Q1. Read Exodus 32:1-14. What had the people done that was so bad?
They were worshipping another "god" - the golden calf that they had made. They took off their gold earrings and then Aaron made a golden calf. They're worshipping something made with human hands. And Aaron's defense to Moses was as bad - "24 "I said to them, `Whoever has any gold, let them tear it off.' So they gave it to me, and I threw it into the fire, and out came this calf."
God had delivered the people from slavery, protected them from the plagues, parted the Red Sea, led them in a pillar of cloud by day and in a pillar of fire by night, sent manna from heaven and meat in the form of quails covering the camp and bread on the ground when they were hungry, provided water when they were thirsty, etc. How quickly they forgot, and still wanted something visible. Jesus says in John 20, "Blessed are they who did not see, and yet believed." But, how quickly we also forget, when God answers our prayers, or we don't take notice. And, today, people worship things like the television set, shopping mall, golf game, etc.
Ex 34:14--for you shall not worship any other god, for the LORD, whose name is Jealous, is a jealous God--
De 4:39 "Know therefore today, and take it to your heart, that the LORD, He is God in heaven above and on the earth below; there is no other.
How can a loving God be angry?
Righteous anger.
God is holy. God is Light, and in Him there is no darkness at all. (1 John 1:5)
Deuteronomy 23:14 says "He must not see anything indecent among you or He will turn away from you."
Is God's sentence to destroy Israel and raise up a new nation through Moses justified?
Yes. God is just...
Deuteronomy 32:4 "The Rock! His work is perfect, For all His ways are just; A God of faithfulness and without injustice, Righteous and upright is He.