You don't need to apply for a new visa you get a visa extention for a year based on marriage on your current O visa.
You can live at any address you just need to register where your living so you'll need mums book or a copy of it and I'd imagine a letter from your wife and mother saying your living there. Take photos of you at the house inside the house with your wife show the house number in at least one photo.
Sorry we rent at the moment so just needed the landlord's book for the process.
You'll probably get a form put in your passport stating your address.
O visa lasts for 3 months then you apply for a years extention if you don't apply for the extention every year you have to reapply from beginning again
From 31 October the 35 current visa exemption is changing to 45 days you can get a 30 day extension at the end of that or just fly out and back again 45 days starts again. It goes back to 30 days march 2023