Birth and Death Process Question (Queuing)

A small shop has two people who can each serve one customer at a time. There is also space for two customers to wait. Anyone who arrives and sees that the shop is full will go to another store. Customers arrive according to a Poisson process of rate $\lambda$ per hour. The amount of time required to serve a customer is exponentially distributed with parameter $\mu$ per hour. Let $X(t)$ be the number of customers in the store at time $t$.

Here are the questions:

1) Evaluate the long-run average values for a) the number of arriving customers per hour who wait before they get served and b) amount of time spent waiting per hour by customers in shop. Express your answer in terms of $\lambda,\mu$, and limiting probabilities $(\pi_0, \pi_1, ... )$.

2) What is the limit as $t \to \infty$ of $P(\;\textrm{nobody enters or leaves the shop during}\;[t,t+3])$? Again, express answer in terms of $\lambda,\mu$, and limiting probabilities.

Here is what I have done so far: for 1a) I know that it is asking for the long-run number of people who wait... the only time people wait is when the store is in state 3 in the long run or state 4... so would this long-run value be $\pi_3 + \pi_4$? It just seems too easy for that to be the answer...

for 2) I tried conditioning on time $t$ but I was unable to proceed after the first step...