Regarding Innovation: Will Villa and Ironworks lose track if you use Innovation's effect?
Villa: Yes, if you choose Innovation to go first. Which means that you still return to your Action phase and get +1 Action, the Villa will however not be in your hand but already played by Innovation (for additional +2 Actions, +1 Buy, +$1).
Ironworks: Ironworks doesn't try to move the card after it is gained, so loose track doesn't really apply. All it does is determining the card's type(s), which should not normally be a problem, but I assume there might be edge cases where it is. So if it is a Band of Misfits that Innovation plays as a Mill, Ironworks will see it as Victory-Action; same if it copies an Island.
Regarding Possession: Which projects are available for the possessed player? What happens if a possessed player buys a project.
Nothing special about this here. It is the Possessee's turn, so their already bought projects work (like Silos) and any projects they can afford and have't bought yet the Possessor can make them buy. Since they are not cards, nothing out of the ordinary happens, the bought projects belong to the Possessee and can be used by them on later turns.
Does Sewer also apply to the “pseudo-trashed” cards of the possessed player?
Yes, the cards are trashed, so Sewer (if bought by the Possessee) is applicable.
It is very clear that you can't discard Copper from Miser, Island and Native Village, isn't it?
To me it is.