There is a long list of questions here which generally makes it hard to answer them. I will start with the basics. The ERC20 Token that you created is stored on the blockchain and you can interact with it by calling different functions like getBalance, sendTransaction.

The way it works is that these tokens are used as a currency for different business models. This is the same concept as nowadays companies offer shares during Initial Public Offering(IPO). Same is the case here. This token is used as a tool to raise money. Companies who want to raise money through this generally publish there whitepapers listing in detail their business model and how they will create value for those who invest in their business

ICO (Initial Coin Offering) is used to distribute this tokens to the investors. For this another contract is written similar to the one used for deploying your ERC20 token, but is much more complex and detailed. This contract is linked to the ERC20 token address. and also contains a price in Ethers for these tokens. Anyone who wants to invest in the business would send Ethers to the ICO Address and would be rewarded tokens accordingly. E.g. 1 Ether = 1000 tokens.

Initially these tokens have zero value in the market. Once the company start their business, these tokens are listed in an crypto-currency exchange. From there tokens get market value.

Transfer method

The transfer method is for a 2 party transfer, where a sender wishes to transfer some tokens to a receiver.

• Sender ➜ transfer(receiver, amount)

Approve and transferFrom method

The approve + transferFrom is for a 3 party transfer, usually, but not necessarily that of an exchange, where the sender wishes to authorise a second party to transfer some tokens on their behalf.

• Sender ➜ approve(exchange, amount)
• Buyer ➜ executes trade on the Exchange
• Exchange ➜ transferFrom(sender, buyer, amount)