Patidesaniyas are offenses that can be cleared through confession, similar to a pacittiya. The difference is that the monastics have to use a specific confession formula to clear the offense: “I have done a blameworthy and unsuitable thing which is to be acknowledged. I acknowledge it.”
There are 4 patidesaniyas for bhikkhus, 8 for bhikkhunis. None of them are shared.
The patidesaniyas for bhikkhus only
(rules 1-4 of 4)
Eating food received from a bhikkhuni
Not sending a bhikkhuni away when she is organizing a meal distribution for the monks
Eating food from families who have been designated by the sangha as “in training” (i.e. should not be approached for alms, because they give so much that they can barely survive themselves)
Living in a dangerous place and having laypeople deliver food there without telling them of the dangers.
Ghee belongs to a group of food that is considered even especially good, and monastics are not supposed to ask for that extra food and then eat it. This is considered being demanding and difficult to support.
If they don’t ask for it and are given some ghee there is no problem eating it.
No, the time of the day has no influence on the offense.
As Anagarika @Sabbamitta explained, the problem is that these foods are considered special, not that monastics ate them in the afternoon.
The list of afternoon allowables is similar but not quite the same: butter, ghee, oil, honey, and sugar.
The sekhiyas are the most minor class of offenses. There are 75 sekhiyas in total, and all of them are shared between bhikkhus and bhikkhunis.
The sekhiyas vary widely between the different early schools which is an indication that they may be a late addition to the patimokkhas.
They mostly deal with monastic etiquette, and cover things like appropriate behavior in town, table manners, and how to teach dhamma.
These are rules for appropriate behavior in public. So they don’t apply in uninhabited places, wilderness areas, private kutis etc.
Monastics are supposed to look calm and composed in public, to be inspiring and a good “advertisement” for the dhamma. What exactly do you find strange about this rule?
The word sekhiya is related to sekkha, “trainee/learner”. Basically, these rules are trainings in sense restraint and mindfulness. The offense is only committed if you break them out of disrespect. If you break them because of lack of mindfulness, there’s no problem. You just keep on training.