Yes, a 90-day report can be done by your wife with your original passport and required documents at your local immigration office. No problem. No POA is required.
Q. If I arrive on a Non Imm O single entry 90 day visa, can I fly out and back again within the validity period of the visa (with a reentry permit)
-> Partially yes, you can leave Thailand and back again with a valid re-entry permit within the period of the first entry stamp you already have, even after the initial visa validity.
Q. and be stamped in for another 90 days?
Not another 90 days. You will be stamped until the same date with the one on the first entry stamp. A re-entry permit can keep the current stamp alive, but cannot add any more days to that.
Funds of 800K baht in a Thai bank account are required for each applicant for a visa/extension based on retirement. In case one of a married foreign couple is applying for an extension based on a dependent on a retirement visa/extension holder, the applicant for dependent is not required to have 800K baht.
Non-O dependent extension will be given with the same expiry date as a primary applicant (you).
If you as the main applicant are using OSS, your wife has to go to OSS, too. Talk with your employer first. She needs documents from your employer too for her extension application anyway.
You need one whole page for an initial in-country visa stamp. You also need a bit more than a half page for the initial 90-day stamp (space depends on how the officer arranges stamps).
If you still have two "visas" pages, not "amendments"/ "endorsements" pages, you may be able to apply for an initial in-country visa. But not enough for a re-entry permit if you need to travel.
Check what type of pages you still have.
Also, check which minimum days policy the local immigration office has for in-country visa applications, 15 working or calendar days. If 15 working days policy, you need to apply for the initial visa within 1 week.
Q. would it be possible that I could extend for another 30 days based on tourism first and later do another extension for 60 days based on Thai family?
-> Yes, possible if you have proof of a relationship. You have to apply for a 30-day tourism extension first at most offices.
Q. can that be done at any immigration office in Thailand or does it have to be only from the local immigration office where my family are based?
-> You apply for an extension at the immigration office that serves your address on TM.30. You can apply for a tourism extension at any office as long as you have TM.30 belonging to that province.
You apply for a family visit extension at the local office that serves the address where your family member lives.
For a family visit extension, you have to have a proof document for your relationship with a direct family member. And you have to bring that member with documents to the immigration office when you apply for it.