First, it is not a singular "spirit world," but a multiplicity of spirit worlds, each of which are home to many different kinds of spirit...For the rest of your questions, I'll insert my responses into your OP quote...
Spirits respond to being evoked.
BHBA: some spirits do respond to being evoked, but most do not. Of those that do, some are going to be helpful, and others are not going to be helpful. That is, some can be invoked, while others can be provoked...and I'm not sure you want to do that...
The Catholic Church and the Orthodox Churches believe that the deceased can be invoked and that they hear our petitions and pray for us and that their prayers are more powerful than the prayers of living people.
BHBA: I agree that those denominations do allow something like that, although I'm not clear on the details.
In Scripture, God is spirit. Angels are spirits. Fairies are spirits. The souls of the deceased are spirits. The pagan Deities are spirits.
BHBA: Yeah, perhaps in the Abrahamic scriptures and traditions, although I think the omnimax creator deity is rather beyond our category of simply "spirit," and maybe the same applies to the angels. But then again, I'm not one who buys into that cosmology/cosmogony. To me, there are lots of different KINDS of spirits, and their being "spirits" says less about them and their variety by forcing things into a single concept, which implies a single substance, structure, origin, etc., than is really the case.
There is an invisible world that influences the material world.
BHBA: There are many 'invisible' worlds that overlap, influence, and are influenced by our 'material' world.
What is your relationship with this world?
BHBA: My relationship to these worlds and their occupants is to interact with them through ceremony, ritual, behavior, etc. I see them as relatives, as kinfolk, regardless of other traits, and try to be respectful to them.
Have you ever seen a Fairy, a ghost, an Angel, or a Deity?
BHBA: I have experienced and interacted with what I consider to be members of the Fae. I have encountered spirits that could be thought of as 'ghosts,' although I am not sure that what I have encountered is really what is thought of in modern conceptions. Angels reflect a certain cosmology/cosmogony that I don't believe in, but I have encountered what appear to be powerful spirits. I used to think I had encountered deities, but now I am doubtful...after all, I'm just a little guy in a vast cosmos, so how would I be able to tell that what I encounter is a deity?
Do you ever talk to your departed loved one's?
BHBA: In this life, I haven't lost anyone particularly close (close family or friends), although I may have encountered a few more distant relatives. However, as an animist, I view all others as kin, relatives to some degree, even when we are different "types" now, or to my experience.
Do spirits visit you in your dreams?
BHBA: Yes.
Do you feel them present inspiring your thoughts and actions?
BHBA: Yes, sometimes.
Have you ever gone into a trance that brought you to the spirit world?
BHBA: In trance and not in trance, in dreams and not in dreams, I have entered into the spirit worlds, or at least interacted with 'spirits'. And those from the spirit world have entered into this one, in my experience.
I'm reading Allan Kardec's Spirits book and he says that spirits are all about us and influence us often and we aren't aware of it.
BHBA: I'm not one for Kardec and the like; I'm doubtful of the cosmology of such beliefs, and what he describes is rarely what I have experienced.