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Hi Fernando, though you have WordPress files inside "example.com/folder", you can set your domain to be "example.com". I think it doesn't matter where you installed WordPress as long as your address is "example.com". And of course, you must be doing your SEO on "example.com".

I think it is more of a WordPress installation issue than an SEO one. You can read more about it here - http://codex.wordpress.org/Giving_WordPress_Its_Own_Directory. I hope this helps.

Hi Alec, recovering from a Google penalty is not an easy process unfortunately. And the Q&A section here wouldn't be enough to explain everything as well. I would suggest going over this article on Moz. It is a very thorough article explaining every steps you need to take to remove manual penalties associated with your website. I hope this helps