Those extra years on Free's contract are fake years (automatically voidable) that were added to stretch out money for cap purposes. Any dead-money hits the cap at some point regardless of whether he is on the team or not. It's easiest to just consider him a free agent.
Weems is restricted.
The Cowboys have an OT name Tony Hills that is a 30 year old journeyman from Texas drafted in 2008.
Hawkins is listed at OT, but they might consider him an OG. Obviously, like Weems in 2013, they like him enough to keep him on the 53 all season despite being inactive for all games.
I have no idea what kind of offers Free and Parnell would get in free agency. Parnell is playing at a similar level to Free but Parnell has 4 career starts compared to about 80 for Free. Parnell is likely to get even better while Free is 30 and has had 2 separate injuries this season which could be a sign that he is on the decline. Free will have problems if he has any decline in physical ability. Larry Allen could have declined 50% and still been able to play in the NFL. If Free declines 2% he's probably toast.
I'm certain that 1 of Free or Parnell will be re-signed and 1 will be gone. That makes the swing tackle the big question mark. How confident are they with Weems? Obviously, Hawkins has a ways to go because they signed and kept a 30 year old journeyman over having him as the swing tackle. It guess they can bring Hills to camp and at worse case have him as the swing tackle. He's already been the swing tackle for 4 games this season.