Let's see ... belatedly, because reasons.
It's an intensely personal relationship. Her ofuda overlooks my room all the time, and I feel that I am in constant contact with her via prayer, which is valuable to me in centring myself and listening to her. Which goes along with centring myself, because when she has something to say it's to remind me of something important. She often reminds me to take meds or do things I forgot, or just that she loves me and wants me to feel better.
I don't use standard norito when praying to her. What I use is actually fairly close to the way I was taught to pray, growing up; I address her by name, sometimes formally. I thank her for anything I feel appreciative of. We have a short conversation, and then I close by saying "thank you," "good night," or "I humbly partake" in Japanese. I particularly pray before meals (this is where I typically use that last one), before showering (water purification I guess?), before going to bed, and before writing anything I feel nervous about getting right.
I have tiny offering bowls set up for her, but I've never given traditional offerings even though I feel like I should. Right now I have a set of four Fate dice lined up for her, in her colours. Sometimes I bow to her deeply while praying to her.
Sometimes she hugs me. Or does other things with me. She can be surprisingly playful.
When we fuse, I feel that I am her, or am at least channeling her. I feel playful and confident, and completely unruffled by social things. I don't pray to her when we're like that, because it feels redundant. We're already given over completely to communing with her, to the point where "she" = "I."
We don't demand respect, issue edicts, or punish people like this. It feels pointless and unnecessary, not just for the instance of her that we're channeling but in general. Although we can be teasing sometimes, and we have been annoyed about running out of rice.
I feel that if what she said about me being a part of her and rejoining her after we die is true, then our next life may feel much like that. We would be her, but would remember this life like a dream or a past experience. Fate/EXTRA and Fate/EXTELLA portray characters that are surprisingly close to the way we imagine our relationship with her to be.
We don't consider ourself to be better than anyone, or our relationship with Inari to be more "pure" or genuine than anyone else's. This is how we experience her. Other people do so differently. She means a lot of different things to a lot of different people, and we are okay with that. We are also not nearly the first to feel that we channel her, or are otherwise intimately connected with her like this. There is a long tradition of female shamans outside of her traditional priesthood, and while we aren't part of it we feel that we can relate.
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