Do check out all the posts on our forums about working in Tailand - I'm sure you will find some very useful information that addresses your questions. In short, f you have a genuine degree (verifications are carried out) and a recognised TEFL certification, you would probably have very few problems in finding work in Thailand. generally, the better jobs (pay, conditions, and working environment) are offered in the private sector and by the many large Catholic schools.
Singapore is practically an English L1 speaking country and the language is well catered for by its own nationals. Malasia is not a traditional TEFL teacher destination, while a couple of international chains of High Street language schools are known to operate in Indonesia. As always, a good place to start searching for more info would be Google, and then come back here for recommendations.