I was thinking that if we could consider this LP as a Phase1 of another LP that is only about x by transforming it into a max LP. Then whether it is always feasible depends on the original LP. Since the objective function about the original LP is unknown, it is possible that the optimal z value for this LP is not 0, which means the original LP is not feasible.
Similarly for (b), if the original LP is not bounded, the above Phase1 LP is unbounded as well.
Am I on the right track?
The solution $(x,y)=(0,b)$ is feasible. The objective $z = \sum_{j=1}^m y_j \ge \sum_{j=1}^m 0 = 0$, so the problem is bounded.