So the memory issues are gone? It was the String class causing problems?
9 V is ok and at least 500 mA. biggest power consumer is WiFi transmission.
I would like to see a photo of the project, if it is possible. Grove is a very good concept.
1 A is very good.
photo of Arduino with sensors, no fritzing
make sure you did not left EspProxy in FLASHING mode in Atmega and power cycle the board.