After death, what happens to the adhar — I mean mind, vital and subtle physical — when the psychic being returns to the psychic plane for rest?
It is dropped off — unless the being has become strongly individualised on the mental plane or both on the mental and vital. Then it keeps its mental and vital sheaths — otherwise they disintegrate and everything essential is drawn back into the psychic.
Why has the psychic being to pass through the other worlds before reaching its own?
Because they are there in between and because so long as the vital and mental formations are there, you cannot go elsewhere than the mental and vital worlds.
While passing through the mental and vital worlds, does not the psychic draw back the substance from its mental and vital beings in order to use it for the next birth?
It does not necessarily take the same substance as before. If it did, there would be no difference between the past life and the new one.
Does the psychic really take rest in its plane as we do here in the physical world when tired?
It is a different kind of rest.
When does it return to the earth again?
Whenever it is due.
After death, when the vital retires to its vital plane, what does it do there till the psychic calls it back for the next life on the earth?
For most people the vital dissolves after a time as it is not sufficiently formed to be immortal. The soul descending makes a new vital formation suitable for the new life.
Could the vital of a worldly man whose vitality was very strong, like Napoleon’s, be immortal, or only that of him who was far advanced in Yoga?
Only if it is consciously developed and connected with the psychic being.
It is said that when one has left this world one enjoys or suffers according to one’s Karma. In which world is this done?
In whatever worlds you pass through — but it is doubtful whether the statement is more than very partially true.
But which part of us suffers or enjoys when our physical body is no more there?
The vital can suffer, or enjoy in the vital world for a time.