ESP8266 07 hosting a local server (wiring)

You still have GPIO0 connected to GND, that puts the ESP in Flash-mode. After the upload the program starts running, but when you reset it, it will just go into flash-mode again. GPIO0 should be connected to a PULLUP and with a switch to GND.
I see you don't have a voltage divider on the ESP-RX. You should have.