Get a new passport asap! Also keep the copy of the old passport, you need both new and old number. Dubai and Qatar (I assume you are from Doha) , always accommodate the passport urgency. Once you have new passport, submit the new application before the visa deadline.
In rare occasion you might be able to renew your visa now and explain to the authorities that you are on the process of getting a new passport . You might as well get a letter from your embassy that your new passport is on its way.
Nevertheless you need new passport asap.
All you can do-it-yourself. Don’t pay for the services claimed by some companies that they can help. Save your $$&
Contact the Thai schools that have international program. They are likely high-end ,in terms of tuition fee for Thai students, who want to have English as a Second language. Search for the schools and contact them directly. Be flexible about the salary and prove them that your teaching style will help the students to be fluent in English. Also,Open to the schools outside Bangkok ,like the small provinces, not big cities or the places that crowded with expats.
Also making Thai friends through internet/social media and you may ask for more information. You might not end up with Ed visa, but business visa, for instance.
Start Learning Thai culture and language now to prove your future employer(s)/ business partner(s) that you are serious. Also start making TokTok clips and make it viral (in good term) that can charm the viewers as soon as possible. Remember !every employer want the best employees not just a plain ‘Farang’
The 30 day visa is quite straight forward. Don’t wait until last minute or expect to extend your visit while you are in Thailand. Day 28or 29 you should go to the neighbor country to get stamped for leaving country and cross the border back to Thailand to get another 30 day visa.
Wet, wear and tear passport is very common found in the frequently travelled people. As long as the entry data and the validation date can be readable, you are fine.