This answer suggests to do Munkres Topology for the GRE Subject Test in Mathematics: recommending books for GRE math subject test
1. Up to approximately which chapter is needed for the GRE?
Of course only ETS can say for sure. But I believe those who have studied topology will be able to have a good guess.
2. I just found out that Real Analysis by Royden and Fitzpatrick has sections on Topology. What's the difference between their sections and Munkres Topology?
I mean, is one more detailed than the other? Could Royden and Fitzpatrick Real Analysis' sections on Topology perhaps suffice for the GRE?
I guess Munkres Topology is broader or more detailed while Royden and Fitzpatrick cover the parts needed for real analysis or something.
For reference, here are the tables of contents:
Real Analysis by Royden and Fitzpatrick