I need help with /execute

To fix the command:

• @e[type=Player] can just be @a
• There is no air with a data value of 1, so the detect will never succeed; it should be 0
• The data value in /fill should come before the old block handling mode

So your command should be:

execute @a ~ ~ ~ detect ~ ~-2 ~ air 0 fill ~-2 ~-1 ~-2 ~1 ~-1 ~1 barrier 0 destroy

I'm not sure if this really does what you want it to though. There is no way to execute two separate commands in a command block, nor is there any way to have a delay in a single block.

Detect syntax:

    /detect <x1> <y1> <z1> <x2> <y2> <z2> <TileName> <dataValue>

The detect command needs block datavalue as well as the ID for the block. The only valid metadata for air is 0. 1 will cause the detect to always return false because minecraft cannot find air with datavalue 1.

Fill syntax:

    /fill <x1> <y1> <z1> <x2> <y2> <z2> <TileName> [dataValue] [oldBlockHandling] [dataTag]

For the fill command, you just mixed up the dataValue and oldBlockHandling.

Final command should be:

    /execute @e[type=Player] ~ ~ ~ detect ~ ~-2 ~ air 0 fill ~-2 ~-1 ~-2 ~1 ~-1 ~1 barrier 0 destroy

Scoreboard Setup:

/scoreboard objectives add LivingTime dummy

Inside of a fast clock (20 times per second clock):

/execute @a ~ ~ ~ detect ~ ~-2 ~ air 0 summon ArmorStand ~ ~ ~ {CustomName:"Target", Marker:1, Invisible:1}
/execute @e[type=ArmorStand,name=Target] fill ~-2 ~-1 ~-2 ~1 ~-1 ~1 barrier 0 destroy
/scoreboard players add @e[type=ArmorStand,name=Target] LivingTime 1
/execute @e[type=ArmorStand,name=Target,score_LivingTime_min=20] fill ~-2 ~-1 ~-2 ~1 ~-1 ~1 air 0 destroy
/kill @e[type=ArmorStand,name=Target,score_LivingTime_min=20]

The first command (ignoring the setup command) summons an armor stand with a custom name of Target at every player who has a air block 2 blocks below them. The next command fills the area 2 blocks below every armor stand that has a custom name of Target. In the third command, the LivingTime for every armor stand is incremented and when LivingTime is at least 20, the area 2 blocks below is replaced by air and the armor stand is killed, removing its LivingTime.