Hi Neil,
Thanks for posting this issue. You are right, image alignment does not work out-of-the box right now. The image gets a class “align-right”, “align-left” etc, which means you have to tweak the css to make it work. You already can change the classnames if you wish, see movie in the plugin options for explanation.
In the next update I will add inline styling as a feature and make it the default behavior. In the options file, you can then change it back to the current behavior, which is considered to be the best practice.
It is not true that images get their own p tag. However, they will always be placed inside a p tag, this tag can contain text as well. This is done to keep styling consistent. Please let me know if this is undesirable.