Does a person's fasting become invalidated, necessitating the making up of days, if they, suffering from severe obsessive doubts about the intention or uttering words displeasing to Allah while fasting, experience this, knowing that they find extreme difficulty in performing acts of worship due to these obsessive doubts?

It is not permissible to surrender to the whisperings of Satan during acts of worship, for they are among his ploys to divert the righteous from the remembrance of Allah. The cure for this is to completely disregard them. Intention resides in the heart, and a single intention is sufficient for performing an act of worship. There is no need to vocalize it or renew it unless it is deliberately rejected. What you have mentioned regarding your actions indicates that you are far from worshipping Satan, and Satan's whisperings in this regard aim to make you abandon the worship of Allah, so do not obey him. Committing sins such as backbiting does not invalidate the fast, but one must repent to Allah for them.