Hi.
I bought Arduino Uno R3 and Nodemcu ESP8266.

Can I use Nodemcu just for connecting to internet and do all my stuff on Arduino?
I think, if exists some library (like Ethernet), when I can send and read data from internet, but uploading code to Arduino and not to Nodemcu.
Thanks.
The short answer is yes, but you can't get out of uploading code to the NodeMCU. You will have to programme it so that it will be able to talk to both Internet and Arduino and, in the course of doing that, you will probably conclude that what you propose is a pretty stupid idea.
The NodeMCU can do the same things as a Uno, and more. It is faster, and has more memory. It doesn't have as many pins, so you can't connect it to many things. This may mean that the first thing to disconnect it from is that redundant Uno, which may be better employed elsewhere.
You have the NodeMCU in your hand, but if you really need the Uno, you would probably have been better off with something else of the ESP8266 family.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=2ahUKEwjplteuxqbdAhVOdt4KHR4YBAkQFjAAegQIABAB&url=https%3A%2F%2Ftttapa.github.io%2FESP8266%2FChap01%2520-%2520ESP8266.html&usg=AOvVaw23hIXXZyWgotEobOyFW4fI