Basically you download the theme, unzip the package, then inside that you unzip the actual theme file encounters.zip and then you should get a folder “encounters” which contains all the theme files inside that (you will know when you see the style.css file there). Using an FTP program, you upload the encounters folder to your WordPress “themes” folder which should replace the existing theme files.
As for affecting plugins…if you have encounters already running and you have no problems, you should be OK.
However, before you do any of this, I recommend you download your current theme “encounters” folder somewhere on your computer as a backup…just in case for some reason you need to go back to it.