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1) I haven't had login issues.
2) I only have two data points, but the reviews in each of my applications were fast, within a few hours.
3) I would put Global Entry since this is "e-Gate for Global Entry". NIA is unlikely to know what SENTRI or NEXUS are. (They're barely familiar with Global Entry.)
4) No, but I don't have SENTRI or NEXUS, only Global Entry. Given the number of people signed up for e-Gate for Global Entry, my guess is that you're the first person having applied with a SENTRI card. Perhaps there are others here with a NEXUS card who could provide some insight.
5) I would wait until the application has been approved and then go to the e-Gate enrollment desk at TPE with your approval information. A SENTRI card presents the same as a NEXUS or Global Entry card, and the format of the KTN is compatible. It's just that the name at the top is different. If the NIA employee has a reference image, my guess is that it's chabuduo enough to work.