I think you're probably using Internet Explorer, and there is a known issue with the editor used by WordPress that will make the images disappear like you described if you dont' put content between each image. The problem has been reported to our developers, but it's not a simple fix and I'm not sure exactly when we can get that updated. We are working on it though! In the mean time, can you try placing some content between each image to see if that helps? It may also help work around the problem to try a different browser until the issue can be fixed.
The most reliable way to re-position a photo is to delete it and re-insert it. However, you may be able to click on it and drag it into another location. If clicking and dragging the image into a new spot doesn't work well in your browser, please try deleting and re-inserting it. I would recommend writing content first and adding the images last if you can.