Can people cross the border to another country yet?

Where is he? I know several people who have gone as tourists to Mexico over the past year. Flights to Europe are more complicated- but not impossible. You really need to give us more information about where you are and where he is. 

Generally no. Given the pandemic etc. 

It depends on what country you're in and what border you want to cross. Many borders remain closed. You can check current restrictions at: https://www.kayak.com/travel-restrictions

That depends what countries are involved. You left that info out.