Is it safe to power Arduino project using a power bank and wall charger?
Yes you can.  A promini will run very well on 5V from a wallwart.  Connect 5V to VCC (not RAW or VIN).  You can also find wallwarts with 2.1mm/5.5mm plugs, and a mating barrel jack adapter that ends in screw terminals so you don't have to try hacking up a USB cable.

Power bank, you will have to play games to convince it that something is connected and drawing sufficient current to keep it turned on.

Wallwart example  https://www.mpja.com/5-Volt-DC-Plug-Power-Supply-4A-Regulated/productinfo/18520+PS/

Barrel jack to screw terminal adapter example  https://www.mpja.com/55_21mm-Power-Jack-Screw-Terminals/productinfo/19454+PL/