8266 ESP-01 (stand alone) connect to Wi-Fi but not to Blynk

First things first, uninstall this library and install 0.6.1 instead and re-test.

In UART mode, what does your serial monitor show?

Try disconnecting the LED and re-testing.

Incidentally, your sketch shows no code to control the LED attached to GPIO2, so I assume that you are planning on using digital pins for your app widgets.
Once you have your current code working, you should forget digital pins and switch to virtual pins for your actual project.

Read this:

Pete.