There is no API or API service. There is an application called MetaTrader which is used via a broker for doing Trading.
MetaTrader is free but you will have to open up an account with a broker for the trading.
MetaTrader also has a programing language called MQL which is used to make your own Indicators and to make automated algorithmic trading programs called Expert Advisors.
I suggest you do some reading of the online manuals and documentation:
If API Service does not exist, myfxbook uses what?
Those are broker services for the MetaTrader Server, not for the MetaTrader Terminal. They are not available for normal users like us. Only for brokerage services and special cases. They are also very expensive.
Thank you Fernando Carreiro