There is no main phase between the combat phases. You move from the first combat phase directly into the second combat phase.

The ability of the emblem can target any creature you control, not just one that's tapped.

If the target of the emblem's ability becomes an illegal target by the time the ability tries to resolve, the ability won't resolve and none of its effects will happen. You won't get an additional combat phase.

If you have more than one of Zariel's emblem, the abilities will each trigger at the end of the first combat phase on your turn. You can choose the same creature as the target of each ability. Those targets will untap before any additional combats. No creatures will untap between the first additional combat and the second additional combat (or between the second and third, and so on, and wow, how long was Zariel under your control?!)