I actually talk about this a lot in the below post if you want more detail.
http://my.reddit.com/r/AskHistorians/comments/1m5gfc/what_was_the_city_of_rome_like_in_the_dark_ages/
However in the interest of giving you some quick answers:
- Archaeologically, it seems that the population decrease was more uniform from 5th-7th centuries (even during the drastic descent of the Gothic Wars), and from 8th onward as the population grew again, it grew non-uniformly around the Campus Martius and near the Vatican.
- Abandoned buildings were everywhere, and would be quarried for new structures (if you're rich) or still-standing brick/stone walls and foundations would be incorporated as aspects of wooden structures built over them (if you weren't rich).
- To the best of my knowledge, we don't really have any firm knowledge of housing prices or the housing market in this era. However I believe Theodoric issued some laws regarding the clearance of dangerous ruins throughout large parts of the city.
- Likely the residential buildings were abandoned, and if still structurally sound, reoccupied by "squatters" although that word implies the existence of laws that suggests that the original ownership rights to an abandoned property were still worth something. The new reality of post-Gothic War Rome would suggest otherwise. It would definitely not be auctioned off or seized or demolished by the government. Any demolition or reuse would likely be privately done.