The rule for melting stuff is the following:"Anything will be affected by magma only if it and the magma are on the same tile".
Adjacent tiles do not count.This applies to doors, floodgates, hatches, pumps etc
and to all attached mechanisms.
To avoid a door breaking all mechanisms inserted in it
and the door must be magma-proof(that means bauxite-only mechanisms in vanilla).
The only exception is when the object considered is made of wood, in that case being near to magma (still unsure how close-for how long) will cause it to burn after a brief time.
About disposing of water:
I think you better change the method slightly.
Make a large chamber, 3 z-level high.
On bottom level you put magma in.
Middle level is empty.
On top level you let water in, and the whole floor is replaced by a lever activated-brigde.
When both bottom and top chambers are full, close floodgates and pull lever to open bridge.
Thus water gets dropped on magma, hopefully leaving no excess.
Then lower bridge and open access shaft.
EDIT: I just noticed the page you linked to was named "no-bauxite" obsidian farming, so I assume you have no bauxite.
Instead of magmaproof floodgates with bauxite mechanisms, you can use this design:
# wall
M where magma comes from
m where magma should go
pP pumps, uppercase means output tile.
. channeled area
+ floor
g gear assembly that provides power to pumps
z-level 0
######
##..##
#gpp##
##PP##
mmmmm
z-level -1
##MM##
##MM##
######
######
######
As long as pumps aren't made out of wood this design will work fine without need of bauxite (make pipes and corks out of metal, any metal is good).
Toggle the gear assembly to "open/close" this pseudo-floodgate.