Initiative tracker

Nobody gets skipped, which is the whole reason this was worth building carefully. Most trackers keep whose turn it is as a position in the list; when a combatant leaves, the list shrinks underneath that position and it silently points at the next one, who then never acts.

Here the turn is held by the identity of whoever is acting. Remove someone earlier in the order and the same person keeps the turn; remove the one acting and the turn passes to whoever was next, exactly as if their turn had ended; remove the last one and it wraps to the top and the round advances.

Only when the turn wraps back to the top, which is the actual rule and the thing that gets lost on paper.

Going back a turn undoes it, including stepping the round back when it crosses the top in reverse. Without that, a couple of corrections would inflate the counter on their own.

They are not. Two combatants on the same initiative stay in the order you typed them, because the rule book leaves the decision to the table: reroll, higher Dexterity, or whatever the group prefers.

Inventing a rule here would be deciding on behalf of people who are sitting at the table and can decide for themselves. If you want a different order, change the number and the line moves.

No. The whole order lives in the page: nothing is sent to a server, nothing is stored, and reloading loses it.

That is fine for one fight, which is what it is for. For a campaign, the initiative order is the least of what you would want to keep anyway.