Yes, Exhibit items can be traded like other items.
From the Curse of the Dark Pharaoh rules:
The Exhibit Item cards represent the ancient Egyptian artifacts
brought to Arkham as part of the "Legacy of the
Pharaohs" museum exhibit. They are similar to Unique Items,
but have no monetary value and can only be gained through
Arkham, Other World, and ...
Investigator cards are explained in the Arkham Horror rulebook.
They are briefly mentioned on page 2 under Game Components and Preparation, and are covered in more detail on page 3 under Investigator Cards:
The small cards included in Arkham Horror are called
investigator cards. They represent useful allies the investigators
may meet and items they ...
Since an investigator gets to roll to see if they lose a Cursed or Blessed status on the upkeep after losing their stamina, they won't get stuck in an infinite loop. If a person is worried about not being able to do anything because of their curse, they can use their Encounter at St. Mary's to simply heal one. Their health will go from 1 to 2, then back to ...
Delayed means two things
The investigator cannot move during his turn
The investigator does not receive movement points during his turn
Everything else is still on. You'd get your normal encounter for the area you are in, you can trade items, etc.
Arrested is worse.
Yes, you would miss your entire next turn, including the encounter. Thereby effectively ...
The FAQ covers this. You make your evade check first, and then monsters.
Q: At the end of your Movement Phase, do you fight monsters
before making the Evade check against Martial Law
to see if you are arrested or after?
A: After the Evade check against Martial Law.