Here is an overview of the gates used in the questions:
- What happens when you apply a Hadamard gate on the plus state in matrix representation? How does that look on the Bloch sphere?
- What if you do an X gate on the 0 state? And on the -? What does that look like on the Bloch Sphere?
The effects on the Bloch sphere can be seen above .
- Try multiplying the following matrices: HZH. To what gate is the resulting matrix equal? Applying this matrix to a state is the same as Hadamard, then a Z gate, and then a Hadamard on a state. Try this on the 0 state, on the Bloch sphere. Can you figure out why HZH is equal to some other gate?
HZH operated on the 0 state looks as follows on the Bloch sphere:
Now we see why this is identical to the X gate. 
- What does the truth table of the CNOT gate look like?
 Fun simulation tool for simple gate operations on the Bloch sphere: https://javafxpert.github.io/grok-bloch/