[Ethereum] Create an Ethereum wallet with React Native for single token

It sounds confusing and basing on the version of web3 you have the syntax is different. According to the error you got at the first place seems like you are using web3 1.0. However the instance code is for the version 0.2.x.x

Just to clarify, this is how your code will look like in case you're using web3 1.0

import Web3 from 'web3';

const web3 = new Web3(Web3.givenProvider || "http://localhost:8545");
web3.eth.getAccounts().then(console.log);

So basically you create an instance of web3 with the givenProvider (in case you're using metamask or mist) or with the local. Then you get your accounts.

In case you're using the old version of web3 the code is slightly different:

import Web3 from 'web3';

let web3 = null;
if (typeof web3 !== 'undefined') {
  web3 = new Web3(web3.currentProvider);
} else {
  // set the provider you want from Web3.providers
  web3 = new Web3(new Web3.providers.HttpProvider("http://localhost:8545"));
}

web3.eth.getAccounts(callback(error, result){ console.log(result) })

There is some documentation about React Native that will help you understand why some packages are not possible to be included into React Native applications.

if the package depends on Node standard library APIs, you will not be able to use it with Expo. The Node standard library is a set of functionality implemented largely in C++ that exposes functions to JavaScript that aren't part of the JavaScript language specification, such as the ability to read and write to your filesystem. React Native, and by extension Expo, do not include the Node standard library, just like Chrome and Firefox do not include it. JavaScript is a language that is used in many contexts, from mobile apps (in our case), to servers, and of course on websites. These contexts all include their own runtime environments that expose different APIs to JavaScript, depending on what makes sense in the context. ref

That said, you can try to include the dist files instead of the package. When you include the package via Nodejs, it will be compiled (if it's required) and possibly use some Node standard libraries.

You can find the web3 dist here, and since it's pure JavaScript (that will run in the browser), it should work also in React Native, according to this page.