Minecraft – Summon fireball going same direction as arrow

First, set a row of Command blocks plugged into a clock, testing for the Player approximate roation:

rotation can be tested for using the target selector arguments ry, rym, rx, and rxm, denoting the maximum and minimum view angle in the horizontal (east, south, etc.) and vertical (up, down) direction, respectively.

For example, to test for someone looking South (=0±22), use

testfor @a[ry=22,rym=-22]

(source here)

Then, for each command block set a command to be triggered if the output is true:

/execute @a[SomeSelector] ~ ~ ~ summon Zombie x y z {YourNBTTag}

Instead of x y z put the relative coordinates you want (for each CMD block pair a different set).
That would be, 4 * 2 or 8 * 2 CMD blocks altogether, depending on the accuracy you want.

you have just about everything you need, all you have to do is combine these commands:

/scoreboard players set @a InCar 1 {RootVehicle:{Entity:{id:"MinecartRideable"}}}
/scoreboard players set @a InHand 1 {SelectedItemSlot:1,Inventory:[{Slot:1b,id:"minecraft:stone"}]}

into:

/scoreboard players set @a eject 1 {RootVehicle:{Entity:{id:"MinecartRideable"}},SelectedItemSlot:1,Inventory:[{Slot:1b,id:"minecraft:stone"}]}

then every player that has a eject score of one (or more) is riding a minecart and has a stone selected in their hot-bar

if this doesn't help, let me know, I'll see what I can do

note: ~ in /tp teleports relative to the player/entity, /teleport is relative to the command block (or person executing)