Why is this battery rated over 5 minutes instead of 15?

Because that is the window the UPS series is designed around. CSB rates the UPS line at the 5-minute discharge to 9.6 volts, which mirrors how modern rack UPS systems ride through: minutes of heavy draw before a generator takes over or the shutdown scripts finish. The 15-minute figure is published too, 43.5 watts per cell, so the battery can be compared directly against 15-minute-rated models when a tray spec calls for it.

UPS12580 F2 or HR1234W F2 in the same footprint?

The cases match to the millimeter, so the tray takes either. The UPS12580 carries roughly a quarter more output at the 15-minute rate and a heavier plate set, and it costs accordingly. Replacing like for like keeps the string balanced, so match the series already in the tray; step up to the UPS12580 only when the whole set changes together and the load has grown into it.

Should I replace one battery or the whole tray?

The whole tray, almost always. UPS batteries age together under identical float and temperature, and one fresh unit wired among tired ones gets dragged toward their condition while masking the tray's true state from the self-test. The exception is a documented single-unit failure in a young set. If budget forces a partial swap, tell us the set's age and we will give you a straight recommendation rather than sell you one battery twice.