That’s what you do online. Every visa is done online with the Thai embassy of your current location. Embassies are outside of Thailand.
And nobody can tell you how long YOUR application will take. It depends on how fast they work and how many applications they currently have. Can be a few days or 2 weeks. Maybe even more.
And: I don’t know what a family visa is. Maybe you should lookup the possibilities on the immigration.gov.th site
Yes. Mine is … don’t know … I got it about 2015. Then you get a yearly extension at your immigration. Costs 1900 and needs a few papers plus some time to wait in line (max 30 minutes in Buriram, but I’ve heard about many hours in Bangkok).
Then you may be out of luck. You would need to do that online with the embassy of the country you’re in. But it takes some time. You might be too late.