I created a demo account, but can not add any stocks to the list. The only things I can add or remove are Forex.
Any idea why I can't see other indices?
You are only able to show/hide from the list of symbols/instruments that your broker provides - be that a demo account or a real account. You cannot simply add "stocks" or "indices" if your broker does not offer them.
If you are using the MetaQuotes demo feed, then you will not have stocks (only CFDs) nor indices.
You will have to find a Broker that supports real stocks (and not CFDs) and other indices and open up a demo account with them.
I simply need to see the stock changes using a web application. I thought this MQL5 will do what I am after. Do you find a broker while within MQL5?
The same still applies, whether you use the Desktop Application or the Web Interface. What counts is the "Account" you are using, which has to be obtained from a Broker that supports the symbols/instruments that you wish to use.
MetaQuotes is a software company that develops the MetaTrader software. The brokers themselves are numerous and spread out all the world and you find them with the usual method - an Internet search (eg. Google).
However, please note that vast majority of those brokers offer CFD's (of stocks and indices) and only a reduced number actually offer real stocks and indices.