The cat that you saved on b8 should be placed in "My House" in Norune Village, along with everything else you need to complete the house.
If you've gotten the Transfiguration Potion for winning the duel on b8 already, then go into "My House" after you've completed it and go upstairs to your bed. Use the potion on the cat which will turn into Xiao (or whatever you told your mother to name the cat when you triggered the event in "My House" by completing it), who will join your team.
With Xiao on your team, go down to b8. Press "select" to choose which character to use. Pick Xiao. As Xiao, press "X" when the red "!" appears over your head when you get close to the river. Xiao will nimbly leap across the gorge. Tadah!
If there are "?"s stopping you from completing "My House" you need to talk to your mom or "Renee" and ask her what she needs to complete her house. Doing this will open up the "?" slots in "My House". Once you've placed "Renee" in "My House" you can find her either inside, standing in front of "My House", or walking around Norune Village. Note that every time you go into the bird's-eye view by pressing "select" in Norune Village, the game randomly chooses whether certain characters are indoors, standing in front of their houses, or walking around (except those who you cannot move, vendors, and those who hold your items for you), but it's not guaranteed to switch form their current position, everytime you do it it's random so it may choose the same location twice in a row. .
If you need more help in terms of Geroma parts and assembly, I would refer you to one of the links on IGN with basic instructions on Geroma Assembly etc. or the instruction manual if you have that. Or, if all else fails, start over and pay careful attention to what the Fairy King tells you about Geroma assembly after you leave Divine Beast Cave the first time.
However, hopefully in the past three months you've already figured all this out.
