If you move the gallery you will need to update the paths for the current ones to continue working. Once moved though the paths that are created should work for you. You will only have problems with moving the files into your root if your have the exact same page and file names.
When it comes to the margin you should be able to just adjust individual margin value for the left and right to get it positioned where you need it to be. I can see the page you posted and the gallery on it, but I'm not sure how you would like it to look.
You can turn off the tool tip when hovering over the thumbnail by commenting out the line of code that shows it. This code is in the gallery.js file, in here look for this line:
You can comment it out like this: