1. is there a way to write a code on some sort of external memory to be attached to the arduino, and make it download the code and operate the arduino code in a push of a button?
2. is there a way to supply the 5v for the arduino not using a laptop but an external power source?
Yes. Connect regulated +5V to the +5V pin OR connect unregulated 7V to 12V to the Vin pin or the power jack (center pin is +). In both cases the negative side of the power supply goes to Gnd (or the sleeve of the power jack).