Let's see:Hi,
In Babayaga hut, my eidolon pass through a door that lead to another plane.
So, If i understand well, he is sent back to his plane because that plane changing send him more than 100000 feet from his summoner.
But
1 - Does he keep all his hit points or are they reduced by 75% because of the distance from the summoner ?
In addition, the eidolon and the summoner must remain within 100 feet of one another for the eidolon to remain at full strength. If the eidolon is beyond 100 feet but closer than 1,000 feet, its current and maximum hit point totals are reduced by 50%. If the eidolon is more than 1,000 feet away but closer than 10,000 feet, its current and maximum hit point totals are reduced by 75%. If the eidolon is more than 10,000 feet away, it is immediately returned to its home plane.
Technically your eidolon went from "within 100 feet" straight to "more than 10,000 feet away" without passing through the intermediary stages, and those are where its HP would drop, so it should be fine.
2 - Does my summoner has to wait 24 hours to make a ritual to bring him back ?
No, that's only if the eidolon actually dies.
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If it is a gate and not plane shift, and the gate is still open, you shouldn't have any problem.
You can trace the distance through the gate, as it was a normal door.
If instead the passage moves you or your eidolon to another plane but isn't a constantly opened passage Fuzzy-Wuzzy replies is applied.
Yeah. If the gate is still open you use the shortest distance. Consider two people standing next to each other. You could say they are only a foot apart or you could measure the long way around the earth and say they are 24,901 miles from each other. Always use the shortest distance.
Now say we put up an impassable wall between the two people that covers half the planet. Suddenly that long way around distance is the actual distance they would have to go to be together.