Yes it is a live ball and if the kicking team recovers they still have to get the first down and if the defense recovers its a turnover. The ball is live, however, the kicking team cannot regain possession of the ball unless the receiving team touches it first.
Yes they can, although that is almost impossible.
Yes, but only if the ball doesn't cross the line of scrimmage. Once it does, the kicking team can still recover the ball but can't advance it.
Yes! A blocked punt is a fumble simply because it can be advanced by which every team recovers said block. This is different then a punt returner who didn't made the catch (basically, doesn't gain possession of the ball). This is considered a "muff" and can be recovered but not advanced by either team.
As soon as anyone from the kicking team touches the ball, it is considered to be Illegal Touching. The receiving team takes possession of the ball where the Illegal Touch occurred. Just because the ball was touched, it does not mean it is a dead ball. The receiving team can try to get possession of the ball and move it forward. If the punt returner touches the football and loses possession, it can be recovered by the kicking team. However, given the way punts are covered in the NFL, this is unlikely to occur. The punt returner would likely be surrounded by players from the punting team, who typically crowd around the ball so it cannot be returned. The punt returner would most likely let the punting team down the ball and have his team take possession where the Illegal Touch took place.
Only if there was a penalty against the team that blocked the punt, such as offsides.
Yes, this is the reason for a punt.
Receiving team. Same as a catch. You must have possession before its your ball.
It's a touchdown.