Safe to use USB-C Charger (adapter) for Macbook Air 2013?
No, it's not possible to do that. The adapter you have pictured is the Nonda USB-C to USB-A adapter. It is commonly used for connecting older USB-A hardware (such as USB pen drives) to newer USB-C computers.

One of the big differences between USB-A and USB-C is that USB-A does not allow for transferring enough power to charge a laptop (i.e. it is limited to only few watts compared to USB-C). In addition USB-A is used to charge devices from the computer - not the other way around.

I have seen multiple adapters for using old MagSafe chargers with new USB-C computers. Unfortunately, I haven't seen any for charging old MagSafe 2 computers with a USB-C charger.