It depends on the amount you send. If it is up to US$ 1000 it is usually in seconds, if you send more it is usually longer. But sometimes there are glitches. But generally I have been very happy with them.
If you marry a Thai national, she would not automatically be recognized as your wife by the US government for the purpose of entry into the country without a visa. She would need to apply for a visa, such as a spousal visa (CR-1 or IR-1), to enter the US as your spouse. The process of obtaining a spousal visa is complex and very time-consuming (almost two years as it involves both the U.S. State Department and the Department of Homeland Security)If you just want her to come to visit a B-2 tourist visa is sufficient and easier to obtain.