Stuck with blynk code for Arduino nano+esp01 wifi module

That’s a problem, as you will have over-written the factory AT firmware on the ESP-01, so it will no longer be able to act as a WiFi modem for your Nano.
You will need to restore the AT firmware to the ESP-01.

You are also getting this compiler warning:

I’d recommend that you un-install the 3rd party library that neds in _WM and stick with the official Blynk library, and ensure that you’re using version 0.6.1 if you’re using Blynk Legacy, or 1.0.1 if you’re using Blynk IoT.

This error message:

is because you have this line of code in your sketch:

and you ignored this information:

The Arduino Uno and Nano only have one serial port (Serial0) so it’s impossible to connect the ESP-01 module to port Serial1, as it doesn’t exist.

TBH, you’d be better-off throwing the Nano and ESP-01 in the bin, and using either a NodeMCU, Wemos D1 Mini or ESP-32, as these have WiFi built-in, and are also much faster and more powerful than the Nano (and are easier to work with).

If you do want to persist with restoring the AT firmware on the ESP-01 and using it with the Nano then you need to read this (and I’d recommend that you read it ALL)…

Pete.