Answer 1: Make sure you use a separate MT4 for each demo account and do not close them during the trading week. Also make sure you see a smiley face in the upper right hand corner of the chart.
Answer 2: You can manually close open trades. This will not affect the EA. The next time the EA sees a trade opportunity it will place a new trade.
Answer 3: You can upload an EA made by EA Studio back into EA Studio to backtest it or to make changes to it.