Let $B\subset A$ be an inclusion of $C^*$ - algebras. I am having confusions on the existence of a conditional expectation $E: A \to B$. I could see that in general an inclusion need not have any conditional expectation. I couldnt get an example towards this. 

1. But if we consider the inclusion of tracial von Neumann algebras, there exists a unique trace preserving faithful normal conditional expectation. 

2. Is the same true for inclusion of finite von Neumann algebras ? I knw there exists a unique centre valued trace but can we find a scalar valued trace? Because the construction of the conditional expectation for a tracial von Neumann algebras are via the GNS  construction. Is the same true for finite von Neumann algebras also?

3. For a $C^*$ algebra $A$, with $B$ is a Cartan subalgebra, then also there exists  a faithful conditional expectation. 

Is there any unified theorem which tells the existence of a conditional expectation(faithful) for a $C^*$ - algebra inclusion?