While it's hard to give a definite answer, I'll share what many have experienced getting their B2 Visa (or what you call a work permit).
1. In theory the processing time of B2 visa is 15 working days, however, Many people have to wait longer to get the visa.
It depends on many factors such as a person who obtains the visa on your behalf and seasons of year. The person with many years of experience has more connections, knows how to cut corners so... he/she may get the visa for you quicker than others. Season also maters, it might takes a little longer in festive season because there are quite a few public holidays.
2. During the processing time of work permit visa, you can't leave the country because your passport is submitted with your visa application, you're staying without a passport so... you will not be able to exit the country with no passport.
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I need to know, can I pass the border between Nong Khai and Vientiane if my passport expires in 3 months? But I have the certificate from the Russian Consulate