Can you leave heated pool open in winter

Yes.  Leave the heat set at 45 degrees or so.  Warning!  If you lose power and the pumps cannot run, it will cause major damage to all pool equipment and pipes if temps dip below freezing.  Winterize your pool and have no worries.

Yes you can leave it. For safety have a bottled type plug to prevent it from cracking as it freezes.

I would say a big NO! There are a lot of risk factors (and they were mentioned above). You can leave the pool heater turned on but imagine your bill after the winter season. I would suggest installing pool winter cover than take the risk of freezing and ruining your pool

I think that it is fine as long as you do not have long period of below freezing temperature. Most pool heaters have a recommended temperature range that you should stay in. Most recommend not operating the heater if the outside temp is below a certain level. I would say that if you do leave it open all winter, use a solar cover at night to retain the heat built up during the day and use leaf nets whenever the pool is not in use to keep large debris from entering the pool.