Providing power to MCU
Applying 5 V directly to Arduino 5 V line

Yes, it is usually "safe" in that it should not break anything.

The 5 V is neither an input nor an output. It is a supply and that 5 V needs to be provided by something. Normally that's the 5 V from USB. It can also be the output of a 5 V regulator which gets its power from an external 7 - 12 V supply (Vraw).

But since you simply replaced the 5 V line from USB with a different 5 V line, there is no real issue.