You are supposed to transfer your stamps as soon as you get your new passport. You can do this when you apply for anything at the local immigration office. If you wait, you must bring both old and new passports every time you travel out.
You cannot do a 90-day report online until you transfer stamps.
, and if you haven't applied for it with this current series of visa and extensions. 60-day family visit extension is one time per visa (not per yearly extension).
There is no three-month option for Non-O-based extension for retirement. All you can do is, go to the local office together to apply for an extension in February, and ask for an "up-to-1-year" extension matching May one.
The worst thing they would do is say no. Then you will still have the same period of extensions, until each Feb and May.