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.
you also need to check the website of the exact embassy/ consulate you apply for your visa at. Many embassies have their detailed version of requirements.
, if you are not hired by Thai company directly, you can apply for Non-B for business (not employment) with multiple entry on Thai eVisa system. Check the residency requirement at the website of Thai embassy in the country you will stay in when your visa expires
Re-entry permit counter is at the International Gate 2, before you go through passport control. That gate is the easiest to get a re-entry permit. If you go through other international gate, you have to go all the way to the re-entry counter at Gate2 from air side after you get through passport control. Others details are as mentioned already.
Photo is a sample of the sign at Gate 3, after passport control.