I guess you could go to a nearby embassy and apply for a non-o there but you're still going to need money in the bank, although you might be able to use your home bank. You could then open a bank account and transfer the money in for the extension. But if you don't have the money anyway then you'll need to find an agent to accommodate
but when you apply for and are granted a new passport from your home country it will contain the details on your old passport in the biometrics. Similarly if you have 2 passports due to dual nationality. The biometrics embedded in the passports will have details of the other passport
You can apply for another visa from a tourist visa if you have enough time left and qualify for the other visa you want to apply for. It can't be another tourist visa but could be, for example, a retirement visa
there is no 7 day grace period. If their employer is being nice ask them for a letter confirming their last day of work and use that to cancel the work permit and extension in advance then leave the country on or before that date. Overstaying is a really stupid idea
They can leave and return on 60 day visa exempt and they can extend for an additional 30 days at immigration. But before they do the WP holder who i assume is on an extension of stay, needs to cancel that extension of stay. Which means they first need to cancel the work permit and that requires paperwork from the employer
Go to the immigration office today, pay the overstay fine, and purchase a 30 day extension (which will run from when you should have got it). Staying on overstay is a huge risk, any interaction with the police could result in you being arrested, transported to the immigration detention centre, being deported back to your home country at your expense and blacklisted from Thailand