A Genestealer closes a door between itself and a Space Marine in overwatch. Can the Space Marine shoot at the Genestealer or the door?
No, the Space Marine can't shoot at either the Genestealer or the door.
He can't shoot the Genestealer because the overwatch shot comes after the Genestealer has completed its action. Closing the door takes the Genestealer out of the Space Marine's line of sight so it can't be shot.
He can't shoot the door because a Space Marine in overwatch is only allowed to fire at a Genestealer that's just taken an action.
Overwatch represents the Space Marine's split second response to a moving target. He's waiting tensely for a Genestealer to show itself and ignores all other targets, such as doors or features like crates.
On the other hand, if the Space Marine player wanted to spend a command point, he could shoot at the door. Command points represent specific orders to perform extra actions rather than instant snap-shot responses. Spending command points allows him to perform any action provided he has just seen a Genestealer take an action.
With command points the Space Marine could turn, step forward or backward, clear a jam or shoot at a door (any door - it needn't be the one that's just closed).
The penalty for doing this, of course, is that the Space Marine loses overwatch.
If a Space Marine forces a Blip to convert into the line of sight of another Space Marine on overwatch, does the model on overwatch get a shot?
No - the newly-converted Genestealer hasn't taken an action in the Space Marine's line of sight, so there's no chance to shoot.