How does gear improvement work

After having played a few matches:

It seems as though you need the majority (75%+) of the Splat Zone. You definitely do not need anyone in it; I took many from overhead. Taking a Splat Zone means that the whole thing will briefly turn to your ink color, entirely (so if it was, say, 95% your ink, it will now be 100%).

If the zone is currently controlled by the opposing team, when your team covers around 50% of the zone, it will become neutral again so that if either team reaches around 75% coverage, it will fully change (back) to that team's color.

If the control switches from one team to the other, the previous holding team will have time added to their timer so they will have to hold the zone for a longer amount of time if they capture it again. The amount of time added is greater if the current time remaining is low and if the zone was continually held for longer. This extra time is separate from the main score and doesn't count when determining the winner.

All maps have either one or two splat zones. In maps with two zones, control of each zone is the same as usual, but the timer will only count down for a team when that team controls both zones.

To unlock the special amiibo sets of gear you need to increase your level in Splatoon to level 7 which unlocks you the shirt of the amiibo sets once you use the amiibo again after getting to level 7. To complete the set you need to get to level 10 and use the amiibo again to unlock the shoes.

The Callie and Maria amiibos also include a special requirement for you to beat Octo Valley before you are even able to use them. Once you complete Octo Valley both the Callie and Maria amiibo work the exact same way as the other amiibos.