One option is to check the Chiang Mai University website. They have some courses you can take to get an Education visa and they also have a 2 month or so English teaching course which you can take then apply for an English teaching job, for which they will help. There are plenty of visa agencies you can contact and find more options on ED visa or what is suitable for you.
Vietnam just did it. Am sure thailand will follow suit. Especially with this new "business savvy" Govt. That's why the talk. They are sending feelers out to see what the public think. Should do the extension before end of the year, I feel.
I guess you are saying you applied visa many times and didn't get one? Well, in that case, you can try to find some visa agent in Thailand and take their services in presenting your case to the immigration. I definitely think you need someone to write and apply for you!
You are an American citizen? If so you apply for your passport with local passport office. Takes about 3 months. But some places may be faster you need to figure out what is faster. Once you get that, just enter Thailand with your old passport. They will have all data and will let you in.
Evisa through their official e-visa site. Takes minimum 5 working days these days. And you can enter only on the port of entry you speicify in the VISA application. Airline will ask for it at checkin and you show it at immigration when you enter Vietnam along with your passport. DO TAKE THE PRINTOUT.
Yes. You enter Thailand from Vietnam, at the airport you can get a 30 day visa.
You don't need to go out of country and reenter. At chiang mai Immigration offices You can go to fill up a form and extend another 30 days paying 2000 baht.
Yes, generally it is a good idea to have a ticket out of Thailand before 30 days from day of arrival. They may ask for it. Get some temporary cancellable ticket.