Can I change a single entry Non-Immigrant O visa to a multiple entry visa or do I need a re-entry permit?

in a simple sentence you have asked all question to visas, it is not easy to answer, but I try. Visas are normally issued outside Thailand and will let you stay 60day as tourist or 90days under Non Immigrant. Visas have a limited period of validity. Once you in the country you can get extensions at local Thai Immigration. The length is regulated by your original visa. A Tourist visa can be extended for 30days and if necessary for a further 7days, than you have to leave the country. A Non O can be extended for 7days if you can not proof that you qualified for the purpose of your application. In case your application is approved you can get up to one year extension, at the same time you can apply for a multiple re-entry permit, THB3,800.-. If you stay more than 90days you have to notify your address every 90days, this is separate from you visa or extension of stay.