[not an official answer]
Hello Elise,
Only Juniors can use mains power, cf the end of F.4.b. "one power socket at 230 V 50 Hz" Eurobot_General_Rules_1.2_EN_JR.pdf
Only Seniors can use the remote computing and observation device.
I do not know which competition you are participating in, but no, the remote computing device cannot be powered from a wall socket.
A laptop can be placed in the remote computing area, so long as it complies with all the rules (dimensions, weight, etc.)