"For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit: By which also he went and preached unto the spirits in prison;" (1 Peter 3:18-19)  
 
This is the Bible verse that speaks of Christ teaching those in Spirit Prison (which most of Christendom calls Hell) the Gospel. There is no scriptural timeline for this except for the fact that Christ was dead for 3 days before he resurrected. So 7 days is out of the question, he was only dead for 3 days not 7.  
 
Through Latter-day Revelation recorded in Doctrine and Covenants 138 we find additional clarification about what Christ did during that time period of three days: " And I wondered at the words of Peter—wherein he said that the Son of God preached unto the spirits in prison, who sometime were disobedient, when once the long-suffering of God waited in the days of Noah—and how it was possible for him to preach to those spirits and perform the necessary labor among them in so short a time. And as I wondered, my eyes were opened, and my understanding quickened, and I perceived that the Lord went not in person among the wicked and the disobedient who had rejected the truth, to teach them; But behold, from among the righteous, he organized his forces and appointed messengers, clothed with power and authority, and commissioned them to go forth and carry the light of the gospel to them that were in darkness, even to all the spirits of men; and thus was the gospel preached to the dead. And the chosen messengers went forth to declare the acceptable day of the Lord and proclaim liberty to the captives who were bound, even unto all who would repent of their sins and receive the gospel. Thus was the gospel preached to those who had died in their sins, without a knowledge of the truth, or in transgression, having rejected the prophets." (D&C 138 28:32) 
 
Christ did organize the righteous Saints in Paradise while he was in laid in the Tomb and sent them forth to preach the Gospel to the Spirits in Prison. Since that time forward righteous Saints have been preaching the Gospel to those who rejected the prophets in this life and through the cleverness of man never accepted the Gospel or ever heard the Gospel in there lifetime.  
 
As far as Jesus's statement to Mary about not touching him, your guess is as good as mine. I assume that in this perfected state right after the resurrection it would be instant death for a moral with sin to come in contact with something as pure and divine as the resurrected Lord.  
 
Christ ascended up to heaven to sit on the right hand of Heavenly Father as it is recorded in the Gospels, he has a body of flesh and bone perfected just like Heavenly Father.  
 
Christ is not the only resurrected being he is simply the first-fruits of the resurrection. Once again through Latter-day revelation we know that John the Baptist, Peter, James, and John are all resurrected beings, that the Angel Moroni is a Resurrected being as well.  
 
Also remember that hundreds of people resurrected when Christ arose as well, they were seen in the Streets of Jerusalem and spoke with there descendants as recorded in the the Gospels and the Book of Acts. What happened to those beings afterwards is not know.