If your strategy has both a sell order and a buy order you would sell the stock from your portfolio and buy the stock new stock immediately when market opens the next day. Do not wait until the following rebalancing period 1 week later.
I'm using my own backtest for the screenshot below. The date was 3rd November because the simulated orders were created on the 3rd of November. As your rebalancing frequency is set to weekly, the next order will come one week later which is the 10th of November. No orders will be created between the 3rd to 10th of November.
For your second question, the positions are shown on the 3rd of November are before the orders have been executed. The backtester sends out the market orders which you execute based on these positions. So for example if the positions include 10% of Facebook and the orders say sell 10% of Facebook. It will mean you are holding 10% of Facebook on the 3rd of November and you are expected to sell 10% of Facebook the next day on the 4th of November.
Hope this makes sense. Do let me know if you have further questions.