Is the God of Christianity a just God? What does the Bible say about the justice of God? Is He just?
YES
Basically what you're asking has been asked throughout history.

Job 8:3 NIV
Does God pervert justice? Does the Almighty pervert what is right?

The Saints defend God
Throughout the ages of biblical times, the saints have declared with trumpets the Justice of God.

Job 34:12 NIV
It is unthinkable that God would do wrong, that the Almighty would
pervert justice.
Deuteronomy 32:4
He is the Rock, his works are perfect, and all his ways are just. A
faithful God who does no wrong, upright and just is he.
2 Thessalonians 1:6
God is just: He will pay back trouble to those who trouble you
Isaiah 30:18
Yet the LORD longs to be gracious to you; therefore he will rise up to
show you compassion. For the LORD is a God of justice. Blessed are all
who wait for him!
Isaiah 5:16
But the LORD Almighty will be exalted by his justice, and the holy God
will be proved holy by his righteous acts.

Why isn't God doing anything about the evil?
You may then ask, why is there evil in this world? Why are there murders and why are there evil people?
God declares that He will judge every deed.

Ecclesiastes 3:17
I said to myself, “God will bring into judgment both the righteous and
the wicked, for there will be a time for every activity, a time to
judge every deed.”
Revelation 20:13
The sea gave up the dead that were in it, and death and Hades gave up
the dead that were in them, and each person was judged according to
what they had done.

How can God forgive us, if He is Just?
God has declared all people wicked, so how can He forgive anybody?

Romans 3:23 (NIV)
for all have sinned and fall short of the glory of God

Well.. isn't that what this entire story is about.

Romans 3:25-26 (NIV)
25 God presented Christ as a sacrifice of atonement, through the
shedding of his blood—to be received by faith. He did this to
demonstrate his righteousness, because in his forbearance he had left
the sins committed beforehand unpunished— 26 he did it to demonstrate
his righteousness at the present time, so as to be just and the one
who justifies those who have faith in Jesus.