Who can become possessed?Anyone, though non-Baptized people are more succeptable.
If completely innocent people can become possessed, why does God allow this?
Because demons have free will (just as God allows you to do evil to innocent people if you wish to do so).
Doesn’t the very act of being possessed take away our free will?Free will is diminished, but many people in a state of possession fight against it (and win). It’s not much different than being in the clutches of other “possessing” influences, such as drug addiction.
Does a possessed person know they are possessed, or do they need to rely on others to get them help?
The possessing demon will usually try to conceal its presence. If a person has knowledge of possession in general, s/he is more likely to suspect. In some (unusual) cases, the situation will be quite obvious to the victim and everyone around him/her.
What is the Church’s position on the entire issue?Each Bishop is responsible for appointing an exorcist within his See (though not all have been good at fulfilling this obligation). The identity of the exorcist is usually not made public knowledge for obvious reasons.
The Church believes that possession can and does occur. But She has also come to the realization that many disorders which were once blamed on possession are, in fact, mental disorders of non-demonic origin.