You will certainly need a degree to teach at an International School. There are however plenty of language schools and rural schools where it may not be an issue.
You can't get a nonB visa for teaching without a job offer and paperwork from the school. Just get a tourist visa and look for a job when you're here. Not having a degree will reduce your options, but it is not insurmountable.
I guess so, if it's a relatively short trip. My then girlfriend did it for 2 years but got sick of the monthly trip to Cambodia. Mind you, marrying a Laotian isn't easy either!