I have downloaded MT4 from another broker. Can I trade with SimpleFX on this MT4?

Yes, you can. The only thing you will have to do is change the Server name in Metatrader settings: just open Menu Tools → Options → Server and enter Server DNS:

SimpleFX Demo: demo-mt4.simplefx.com
SimpleFX Live: live-mt4.simplefx.com

If you use your MetaTrader e.g at your job but it can not connect to your server, most likely , your computer is connected to the Internet via firewall or a proxy-server.

Trading conditions for demo account won’t differ from the ones for live trading account. Quotes on demo accounts are the same as on real trading accounts.