Let's go bullet by bullet through your first set of questions. I'm going to assume that the object in square B fills the square completely and thus blocks LOE/LOS from C to the square behind it. This is not universally true and depends on the object.

1. This is a blast 3 power, and as such, the origin of the blast is actually the caster's square. So no, the blocking terrain does not prevent the cast. However, the blocking square does prevent LOE from the origin of the cast to the square behind the block. However, if the zone is moveable, the zone would end at the end of the caster's turn as it does not have LOE to one of the squares it would affect (see RC 121, moveable zones; H/T BESW). If the zone is not moveable, the square behind the blocking terrain is not part of the zone.

2. Yes it does. In this case the square above and right of B is blocked and not affected, but the square behind B is affected. Again, if it's a moveable zone it ends because it does not have LOE to all affected squares.

3. If the zone is moveable and contains blocking terrain it ends. Moveable zones can't be moved through blocking terrain.

4. The zone moves, the square affected change, but you still can't move it through blocking terrain.

5. You can't move a zone through blocking terrain, so this is moot.

6. If the zone is unmoveable, then no, the introduction of blocking terrain has no affect, as the zone already exists. However, if it is moveable, it definitionally ends on the creator's next turn.

So basically, you've largely got the right of it, but have missed (as I had until I answered this), that moveable zones have specific rules surrounding them that govern this very situation. Moveable zones cannot persist with blocking terrain in them and cannot be moved through them.

Let's go bullet by bullet through your first set of questions. I'm going to assume that the object in square B fills the square completely and thus blocks LOE/LOS from C to the square behind it. This is not universally true and depends on the object.

1. This is a blast 3 power, and as such, the origin of the blast is actually the caster's square. So no, the blocking terrain does not prevent the cast. However, the blocking square does prevent LOE from the origin of the cast to the square behind the block. However, if the zone is moveable, the zone would end at the end of the caster's turn as it does not have LOE to at least one of the squares it would affect (see RC 121, moveable zones; H/T BESW). If the zone is not moveable, the square behind the blocking terrain is not part of the zone.

Note: The above interpretation is reliant on a specific parsing of the phrase "

2. Yes it does. In this case the square above and right of B is blocked and not affected, but the square behind B is affected.

3. If the zone is moveable and contains blocking terrain it ends. Moveable zones can't be moved through blocking terrain.

4. The zone moves, the square affected change, but you still can't move it through blocking terrain.

5. You can't move a zone through blocking terrain, so this is moot.

6. If the zone is unmoveable, then no, the introduction of blocking terrain has no affect, as the zone already exists.

So basically, you've largely got the right of it, but have missed (as I had until I answered this), that moveable zones have specific rules surrounding them that govern this very situation.