Discussion about the brokers (especially suggestions/recommendation of them) are very limited on the forum sorry.
I am recommending to you to find a broker for your senf for example.
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Those are the links for MT5 (but it should be same for MT4):
I want to remind the following links:
MetaTrader 5 Help - Open an Account
MetaTrader 5 Android OS Help - Opening a Demo Account
MetaTrader 5 iPhone/iPad Help - Connecting to an Account and Opening a Demo Account
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Forum on trading, automated trading systems and testing trading strategies
Sergey Golubev, 2017.01.09 05:52
Find a Server by the Broker's Name
Another convenient new feature of MetaTrader 5 is adding brokers' servers by their names. With the previous version, you had to contact your broker to find out the IP address of the trade server or download a special client terminal. Now, you simply enter the name of the broker. The system automatically finds the server with the specified name and adds it to the list.

- www.metatrader5.com
More (MT5) -
Forum on trading, automated trading systems and testing trading strategies
Sergey Golubev, 2017.04.06 18:54
There is no list (does not exist).
I used 'search' to find the threads of MetaQuotes about the brokers here to open demo account with them just to check the symbols/instruments they are proposing.
So, you can see:
And some of them (some of those brokers) are having the following:
Forum on trading, automated trading systems and testing trading strategies
Stock and Equity Charts on MT5 Demo
Alain Verleyen, 2013.04.04 11:52
MT4 can't trade stock. MT5 can but you have to find a broker who provides that.What you are looking for are CFDs, I hope you know the difference.

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Hi, what'is the best best broker with demo account possibility with a large number of stocks and MT4?
Thanks