No, you must be inside the country to apply. You must upload proof that you are in the country, generally your entry stamp in your passport, and you must remain in the country until your visa is issued.
You wouldn't find it on the immigration website because immigration has nothing to do with embassies. All embassies now use the e-visa website for visa applications. I would avoid any embassy in Malaysia as they've gotten very difficult since switching to evisa. There have been some reports from Laos where people have submitted the application, went in to pay (for some reason you're still required to pay in person for the Laos embassies during specific hours) and then they're called to schedule an interview next day. Then they've received the visa in their email before they even got back to their hotel.
But pretty much every embassy says 15 day processing time on their websites.
The only 2 options for the first extension are 800,000 baht in a Thai bank for 2 full months at the time of application, or embassy certified income. If your embassy does not offer this as many do not, your only option is the 800,000 baht in the bank.
You won't find many people who have used this service. You still have to go to immigration and bring all the documents you uploaded, and you have to pay an extra fee on top of the normal 1900 baht for extensions. You could just make a free appointment without any extra fee, or go without an appointment and just pay the 1900 baht.
Your question doesn't make sense because you can only apply for a non-OA visa in your home country through a Thai embassy.
If you entered with a 90 day non-O then the only thing you can apply for while on that is a 1-year extension. Not for a visa, an extension. Not a non-O or a non-OA, an extension.
When you apply for a retirement extension there is not normally any waiting period. The extension is granted same day or next day.
IF for some reason the immigration office gives you an under consideration period, they will stamp your passport with a date to return. You must return on that date to get your full stamp. You can leave before then as long as you purchase a re-entry permit and as long as you return by that date. If you're not back, then you lose it and have to start over from scratch.
Just don't bother filling in any of the not-required fields. Your TDAC has nothing to do with an ongoing ticket. You're not required to fill in visa number, and you're not required to fill in departing flight information. It's called an arrival card and your arrival details are the only required fields.