Transferring data from old 2012 MacBook Air to new MacBook Air.

Depends on what you mean by problems. There will likely be non-Apple apps that are not compatible and will need to be upgraded.

Also, as recommended in Transfer to a new Mac with Migration Assistant - Apple Support you should upgrade the MacBook Air to the latest possible version (macOS Catalina 1015.7). A mid 2012 MacBook Air can be upgraded to Catalina 10.15.7 but no later. See: How to download and install macOS - Apple Support

Yes. See the following Apple Support article for information on migrating to a new Mac: Transfer to a new Mac with Migration Assistant - Apple Support