Simple Random Walk: two questions

One useful book could be Probability and Random Processes 3rd ed, by Grimmett and Stirzaker. Sections 3.9 and 3.10 have material on Simple random walks. For the three questions:

1) I think you can use the hitting time theorem, p.79.

2) Here, you could use theorem (10), p. 78.

3) Eq. (9) on p. 74 gives a formula for the mean number of steps $D_k$, starting from $k$ before hitting one of the absorbing barriers at $0$ and $N$, for $p=1/2$, it is $D_k = k(N-k)$.