Am I entitled to social security after retirement age assuming I will leave the US?
You are eligible for SS benefits once you have paid at least 40 quarters (10 years full time of work) into the system. That applies to you regardless of immigration or citizenship status.
Only US citizens can collect SS benefits abroad (with the sole exception of Canadians). LPRs (Green Card holders) have to reside in the US permanently, otherwise they would lose their immigration status and couldn't collect.
My 401K is close to being maxed out for the year. Should I put my savings in a Vanguard fund or should I open an after-tax account as well? How would you split the two?
Depends on your income. Generally speaking, I would go full out on an IRA as well. If your tax burden is high, that would be a traditional IRA. If your tax burden is low, go for a Roth IRA. Keep in mind that you can access your 401K for a home purchase, penalty free.