well, first off, he has no dice pool for any of those shots =P heavy weapons isn't in the firearms group

but, for the sake of argument, we'll assume you meant skill 4, and we'll assume the missing bullet in the last burst (note 3 short bursts is the rules, which is 9 bullets... presumably one just sorta doesn't count for anything)

so, starts off with 7 dice. against:

[ Spoiler ]

PC 1: 4 skill + 3 attribute -2 recoil = 5 dice

PC 2: 4 skill + 3 attribute - 5 recoil - 2 first extra target = 0 dice. longshot test needed

PC 3: 4 skill + 3 attribute - 9 recoil - 2 first extra target - 2 second extra target = 0 dice. longshot test needed.

a better example, IMO, as it shows the progression better, would be a maxed out elf gun adept: 7(10) agility, 7(10) heavy weapons (LMG specialisation) with a smartlinked gun, for a total of 24 dice to start off. still no recoil compensation

[ Spoiler ]

PC 1: 10 skill + 10 attribute + 2 smartlink + 2 specialisation - 2 recoil = 22 dice

PC 2: 10 skill + 10 attribute + 2 smartlink + 2 specialisation - 5 recoil - 2 first extra target = 17 dice

PC 3: 10 skill + 10 attribute + 2 smartlink + 2 specialisation - 9 recoil - 2 first extra target - 2 second extra target = 11 dice

and, perhaps a more reasonable example? chargen possible even

elven samurai: 6(

agility, 6(7) heavy weapons, smartlink, and specialisation in LMGs, and we'll run two examples: one with no recoil compensation, one with the standard white knight's regular recoil compensation, and one with gyro stabilisation added on:

so, no recoil comp.

[ Spoiler ]

PC 1: 7 skill + 8 attribute + 2 smartlink + 2 specialisation - 2 recoil = 17 dice

PC 2: 7 skill + 8 attribute + 2 smartlink + 2 specialisation - 5 recoil - 2 first extra target = 12 dice

PC 3: 7 skill + 8 attribute + 2 smartlink + 2 specialisation - 9 recoil - 2 first extra target - 2 second extra target = 6 dice

standard white knight (6 points recoil comp)

[ Spoiler ]

PC 1: 7 skill + 8 attribute + 2 smartlink + 2 specialisation = 19 dice (would be 2 points of recoil, but recoil comp negates all)

PC 2: 7 skill + 8 attribute + 2 smartlink + 2 specialisation - 2 first extra target = 17 dice (would be 5 points of recoil, but recoil comp negates all)

PC 3: 7 skill + 8 attribute + 2 smartlink + 2 specialisation - 3 recoil - 2 second extra target = 14 dice (would be 9 points of recoil, but recoil comp negates 6)

and with a gyro stabiliser added on:

[ Spoiler ]

PC 1: 7 skill + 8 attribute + 2 smartlink + 2 specialisation = 19 dice (would be 2 points of recoil, but recoil comp negates all)

PC 2: 7 skill + 8 attribute + 2 smartlink + 2 specialisation - 2 first extra target = 17 dice (would be 5 points of recoil, but recoil comp negates all)

PC 3: 7 skill + 8 attribute + 2 smartlink + 2 specialisation - 2 first extra target - 2 second extra target = 15 dice (would be 9 points of recoil, but recoil comp negates it all)

hope that helps.

[edit] spoilers added to shorten post [/edit]