No, they are not. They're splinters of Honor and/or Cultivation just the same. Most don't pre-date the shattering (Besides all the investiture was reassigned to them anyway); it is irrelevant if the shard is broken beforehand for splinters to form.
As they are from a Virtuosity system, their souls have a lot of Virtuosity in them. Whenever a shard invests in a system, the people who live there gain extra investiture of that shard, be it Preservation, Endowment, or Honor. This is one of the things that differentiates a major shardworld from a minor one.
Arcana is a catch-all, very rarely used (it's been used like twice by people asking wobs, and once in the coppermind). As far as I can tell, it's a less sciencey term, basically the same thing as just calling something magic. Most of these "Arcana" are the result of an Invested Art; we are literally told the Machine was awakened (Not the Nalthian version), which is an invested art. The plants are using an Invested Art, because invested art already means any action that causes something magic. You could probably call a Highstorm an arcana if you want, but the nightmares and the machine are the result of an Invested art and thus are of one. It's like calling Nightblood an arcana, he's just some awakening turned up to 11.
They are not ghosts, as they are not dead. At least not entirely, as a death in the cosmere comprises two parts. You can bring someone back from the first gate, where physical death occurs. (Pretty much every healing magic can do it.) But you can not, bring some back from The Beyond. It just doesn't work. Sometimes you can make a vague echo of a person by filling their corpse with investiture, but that is a whole different process from making a cognitive shadow. You can call making a lifeless Necromancy, though. What The Machine did was capture the souls of the people and use them as fuel. It's somewhere in-between a Fabrial and Nightblood.
(Do you mean the shattering? Or are you referring to Virtuosity splintering herself?) Either way it is plenty of time. Lots of investiture means evolution is speeding up.
The Hijo, probably.
Either
A: The spirits were around before. (You can have splinters of a shard before the shard splinters. Yes, it's confusing)
B: Virtuosity's background magic powered them; they used the ambient investiture to form special weight fields.
C: They just were not on Komashi before Shattering/Splintering.