I'm not sure that guys that keep a slave and a meth lab in the compound where they live are going to be too concerned about destroying a CD. It's not the first thing the cops would notice if they raided the place. It doesn't help Jesse but I actually really hope that the CD gets found for the sake of Drew Sharpe's parents.
I think the immediate conclusion and headline news would be that it was Heisenberg's lab, but once the cops started to untangle everything they would realise that doesn't make sense. Walt's fingerprints were on tank in that lab. Jesses fingerprints were all over it, and in the pit. Even before fingerprints had been checked it should be obvious that Walt can't have been in New Hampshire and the person kept in shackles on the compound.
Regarding the DVD, Jesse the Meth slave had value to the Nazi's (or at least to love sick Todd, who needed him to try to win Lydia's heart with pure, blue meth), the DVD had no value to them and could only do them harm.
Would Marie have known about Jesse describing the Drew Sharpe murder? She was certainly in on some of the confession, but I don't know if she heard that part or had watched the tape.
She was probably the only one besides Hank and Gomie who knew they were working with Jesse. Obviously she would have told the authorities that Jesse was with Hank and Gomie when he briefly arrested Walter, so they would have been looking for Jesse since then. After a while, they would probably have assumed that he was in the same hole as Hank and Gomie somewhere, though they might also wonder if he had double crossed them and helped Walt kill them.
Regarding fingerprints, I wonder how many of Jesse's would actually be in the lab. I believe he wore gloves during all his cooking and cleaning and he and Walt were in the habit of very, thoroughly scrubbing all the equipment after each cook. I'm sure there would be some around, but there might not be so many around that the police couldn't help but find them.
The shackles were left in the clubhouse where Jesse killed Todd and Walt killed the rest of the Nazi's, so the cops might not have connected them to the meth lab, though the overhead leash system in the lab might indicate that someone was being held there. Could they speculate that the Nazi's were holding Walt, he escaped, went to NH to plot his revenge and then returned to carry it out? On the surface, that might seem like the most reasonable explanation.