This is a question to ask your employer's HR Department about. Typically, vesting periods stop when you leave the employment. If you have worked for less than three years for the company when you leave, the contributions don't vest 100% when three years have elapsed. However, there are various rules that 401(k) plans must follow regarding how long the vesting period can be. If I remember correctly, vesting periods as long as five years are permitted but only if at least 20% vests each year till one gets to full vesting after five years of employment, and there might be something similar for three years too.
When you do withdraw your 401(k) money from abroad, I believe that there is a mandatory 30% withholding for federal income tax. In addition to Federal income tax, you will have to pay the 10% penalty for early withdrawal unless you are at least 59.5 years of age. And yes, you can withdraw the money over several years to reduce the tax bite.
In view of the newly-added information in a comment that the OP will still be working for the "same" company, just in a different country (India?), the question that needs to be asked of the HR Department is what rules govern the 401(k) in these specific conditions. The OP might be beginning participation in a different retirement plan which might or might not be linked to the current 401(k) plan. If linked, the vesting after three years of employment might occur (or might not, depending on the details of the linkage). Also, there may be country-specific rules that the OP might need to follow, e.g. I believe that in India, NRIs returning from abroad "permanently" are allowed seven years (or is it three years?) from the date of return to bring all their assets from outside India back to India without any tax consequences in India.