From a Speculative Christian Neoplatonist perspective -
First one has to determine the difference between soul and spirit, and level, which is the nature of the activity. In the Hebraic tradition there is a hierarchy of the soul, but aside from that issue, the question addresses the soul, which is the whole person, rather than the individual spirit which is a component part, a product of the life of the soul.
Q1- Yes spirits exist after we die, and we are free to hang around anywhere.
A1 - The soul can continue after the death of the physical body, although this is not guaranteed, nor even unconditionally permanent ...
Q2- Yes, spirits exist after we die, but we are not allowed to go anywhere else other then the sky or God's asylum.
A2 - Yes (provisionally - see above) and yes we are not allowed ... - if the soul can exist in a post mortem state there has to be a prior condition of existence - so in this sense its 'options' are determined: a paradisical state, a limbic state or an infernal state.
Q3 - Yes, spirits exist but we are not able to see or hear anything, we are in a deadly form, and we'd rise again on the day of judgement, to go to hell or heaven.
A3 - Such is the condition of the animic soul, which passes to Sheol, the Hebrew netherworld. In the Hebrew tradition the soul is 'nefesh' which might be called 'life', it is the 'psyche' of the Greeks and 'anima' of the Latin.
It should be understood that the Greek definition of 'psyche' does not match the Hebraic understanding of 'nefesh'. The Greek view is dualistic, the Hebrew is wholistic.
In death nefesh plays no further part in life. Such is a 'dead soul' - it is not 'active' and has no 'experience' in the sense of 'living' or 'suffering' in a netherworld - it simply ceases to act altogether, so in this sense is 'dead to the world'.
Psychic entities of an advanced degree can see and hear, and interact with the world, but they are a product primarily of the psyche and as such might be likened to a residue.
Classic examples are a room that 'reminds' you of someone, you 'sense his memories or presence' - a presence but no activity - a shade. Further along we have apparitions, which might be likened to an activity without a presence, and then a ghost, with which one can appear to interact. Whether any interchange has actually taken place needs careful investigation ... but this is all speculation ... the realm of spiritualism.
Short answer is avoid everything at this level - its usually serving its own benefit, not (and in some cases most definitely not) yours.
Q4 - No, spirits dont exist, we are like animals, we die and that's it.
A4 - Everything that lives (ie has a self-defining activity) has a soul. The bible refers to man as 'a living soul' (chay nefesh) and animals as a 'living creature' (chay nefesh) - the same word applies.
Q5 - We as spirits exist at God's asylum and we are allowed to go down in the spirited form on special request from god or angels.
A5 - The soul is a nexus of spirit and matter. The soul is not an immaterial autonomous entity that occupies a disposable body (and by which the whole of creation would be equally disposable), the body is the material form of the soul.
Addendum:
Spirits, or rather spiritual beings, do exist and do watch, but they don't interfere of their own volition (which is at their level a sin) they don't act because they don't know the End the Divine holds in view, so to act would be 'wilful' and thus a sin. Hence the saying, 'fools rush in where angels fear to tread'.
Angelic beings are of a higher order and do possess a degree of self-determination (and hence they too can fall). They are servants and primarily messengers, and would require a degree of self-awareness and determination to accomplish their mission - they would not be able to talk, for example, but rather simply recite like a record. Not much use if you dropped the saucepan in surprise and missed what was said. Or more accurately, in Scripture men talk to angels which mean they must possess a degree of cognisance to engage in dialogue.
Thomas
I was brought up Roman Catholic