A blue IRN adopted me about a week and a half ago and my experience with birds is limited to a budgie at age 10 that opened his door and flew away. I also have to say that I would never have intentionally owned an IRN but I am a "stray magnet" with all animals and apparently a complete sucker..

It's a bit of a story but relevant to my confusion, "Monty", arrived in my vege patch 3 mornings in a row whilst I was watering the plants. She/He perched herself inside of a roll of chicken wire surrounding the strawberry plants, but she wasn't eating anything. On the third morning I thought that she must be a lost pet and might be hungry. I grabbed a handful of seeds that we feed the wild birds and she flew down landed on my hand, ate some seeds and then just followed me for about 2 hours. I went to get a towel/cage because by then I was worried for her safety, (most of my neighbours have big, bitey dogs). When I returned she was gone. Next day I had a cage out with food and water in it, in case she came back. As soon as I went out in the morning she flew down from no-where and landed on my head. I put her in the cage which she was none to pleased about and I have felt guilty about ever since. (They do not live in the wild where I live and actually have to be reported to the "pest authority" for housing if spotted in the wild because they are usually escaped pets)
The cage is supposedly big enough for an IRN but not to fly in. I have cats that would have to be shut away to allow her to fly and I am also scared about her getting scared and hurting herself, or not being able to return her to her cage. I have spent a good deal of time every day with her and given her seeds, pellets, fresh fruit and veges, a bit of chicken and egg occasionally. Loves grapes! I was trying to get her comfortable with me before letting her out but am now scared she needs handling/flight or she will loose her tameness. She will take food from my hand sometimes but would not step onto my hand. She walks away from me when my hand is in the cage, but doesn't fly with fright or flap. She/He also seems to do a "display" for me when I sit with her, but she actually is doing it for the reflection in her food dish. His/her display includes eye pinning, holding her "shoulders" out, while she makes a figure 8 shape with her head. She makes a chattering noise at the same time that increases in pitch and repeats. (this is the part that makes me think she might be a he?)
She also walks around the cage in what I think is a playful way when I sit with her but doesn't seem to do that unless she can see me. She is not aggressive but has nipped me twice when I was hand feeding her, it was more like she was tasting me than biting though.. if that makes sense?
I want to do the right thing for her. She is not a baby, I know that, but she may not be mature either. She is blue, with a light blue ring (no dark ring), her beak is red and her feet are white. Her tail is definitely more teal coloured than blue. I will try and upload a photo later.
Any advice in whether I should try and tame her or to build her an aviary to live next to the lovebirds and introducing her to cats???. Any advise in general to determine whether I have a mature female or immature male... and really any other advice from anyone kind enough to read through this saga. Thanks for your time.