Did the sky coach take any damage from the explosion?

There appears to be scorch marks upon the surface. Sky coaches are generally quite sturdy, so a light explosion won't destroy it.

Oh right, I forgot about the two Acrobatics checks.

Acrobatics: 27   20

Eldin notices the two guys hold on to the end of the rope. Eldin is neither very strong nor very heavy so he knows he'd get beaten in a raw pulling match. So just as the two guys start to pull, Eldin burns the rope attached to him with a small version of Fire Bolt, causing the two figures to loose their balance for a bit.
(This was written with RP in mind rather than any mechanical benefit.)

Ith casts magic missile, targeting the strings of the crossbows. The two holding Eldin and the one who fired at him.  So that's DCF #1, #2 , and # 5.

Damage  from each missile incase its needed 3, 3, 4.

Boo begins to shrink to half her size. The ropes begin to slip away and untangle from her, but the bolts in her remain tugging as she falls further. She takes 10 damage from the sudden drop and the bolts ripping inside her but now is no longer restrained. The one holding Boo's ropes gestures to the others, letting go of the ropes as Boo begins to fall, hurtling into the chasm that is between the spires of Sharn. (Boo: Falling!)

"Ouchie!" Boo whimpers in pain as she plummets to certain death or so she hopes the DCF's would/will assume, freeing themselves to concentrate on bigger fish they need to fry...

Boo smiles, the wind rushing up against her face as she falls thinking, 'hell yeah... I've always wanted to be Pixie,' as once she drops below the sky coach and no longer restrained she activates her Winged Boots and flies directly underneath the sky coach's hall looking for cover, having no wish to be caught in the middle of a crossfire between the two sides.

--Boo's Flight of the Pixie Mix Music--

The Pixie sized (sort of) Boo's flight plan is to continue flying out of sight under the hull and then out the other (opposite) side with the idea to be out of the direct line of sight of both her gang and the DCF's! Boo, when she gets around and in place and gets a bead on the sky coach diver, she targets him with a Sacred Flame 8 Damage, Dex Sav 14. Keeping to the side of the hull for cover and duck back out of sight in a 'driver blind spot' etc. if possible from the driver once her cantrip is cast.

@Boo

(I'm going to rule that since you were falling for a round, and since Feather Fall slows your descent to 60 feet, your fly movement with your winged boots would not get you to a place in order to see the targets on the ship. You can dash in order to do so, or stay beneath where the sky coach is. In addition, both the sky coach and lightning rail are moving horizontally at a decent speed too, so you will need to keep up in that fashion...)

INITIATIVE TRACKER

Boo starts to fly under the sky coach but sadly discovers her 25' movement is insufficient to match either the sky coach or return back to the faster-moving lightning rail! So Boo watches them (vehicles) both pass her by unable to keep up. With no other option, she looks for a place to land and makes her way to the hideout as best she can to meet up with the others... hopefully later.

(I think Ith moved already if I m 'out mistaken) 

Majin will fire at the sword guy again Attack: 15 Damage: 6 and again Attack: 18 Damage: 5

He will then use is action surge to throw his own bomb into the carriage 

(I was waiting to see what Majin was doing before applying Ith's turn)

Majin fires a pair of shots at the wounded figure. The first shot is dodged, but the second catches them in the shoulder. They nearly drop their scimitar, but are still standing. (DCF #6: 28 damage) The Bomb is then hurled at the carriage, getting half of the DCFs since they split up slightly after the prior explosion. 
Dexterity Saving Throws: DCF #1 20, DCF #2 16, DCF #3 10

One of the figures is caught in the explosion, taking 7 fire damage. (DCF #3: 7 damage)

Ith casts a Magic Missile. The two ropes impaled into Eldin are broken by the spell, as the final bolt strikes into the one that shot at them. (DCF #5: 8 damage)

INITIATIVE TRACKER

Eldin decides it will be best to get rid of the guys with crossbows. Eldin picks out the one among the two who has taken more damage and fires a bout of flame at them (Fire Bolt)

Hit: 8 Dmg: 5 Fire

Carrick will take two more shots at DCF #6 and then duck back into the carriage so that he's not just standing there.

Attack: 24 Damage: 4

Attack: 19 Damage: 4

Carrick will swear silenty when he sees that he didn't really do that much. 

Eldin hurls a bolt of flame, but the figure manages to duck and weave away from the fire, avoiding taking damage.

Carrick double shots at the most wounded figure, causing them some severe wounds. They appear to be near collapse. (DCF #6: 36 damage)

Edrick is still on the task at hand...

DCF 1 & 2, with their ropes now broken, reload their crossbows and fire off standard bolts at Ith in retaliation.
Crossbow, Heavy vs. Ith: Attack: 15 Damage: 6 piercing damage.
Crossbow, Heavy vs. Ith: Attack: 10 Damage: 8 piercing damage.

Ith manages to evade the first shot, but the second impales into the thigh. (Ith: 17/38 HP) Please make a concentration check for the enlarge/reduce.

DCF 3, 4, & 5 provide cover fire for their injured companion.
Crossbow, Heavy vs. Eldin: Attack: 19 Damage: 5 piercing damage.
Crossbow, Heavy vs. Eldin: Attack: 20 Damage: 7 piercing damage.
Crossbow, Heavy vs. Carrick: Attack: 25 Damage: 8 piercing damage.

Eldin is struck by one of the bolts, catching in his hip. (Eldin: 25/40 HP)

Carrick is caught by a fairly nasty shot, getting into the gut. (Carrick: 35/54 HP)

DCF 6 ducks and backs away, headed towards the sky coach's covered driver's area to get away from the attacks of the party.

As Boo attempts to catch up, she notes that a sky coach is swooping in behind her. Looks like their taxi service has come back for some assistance. "Hop on!" Biff calls to the shrunken flying halfling.

INITIATIVE TRACKER

If Eldin still has a reaction, he'd like to use it to cast Hellish Rebuke on the one that hit him. DC14 DEX save to take 4 Fire damage or half as much on successful save.

DCF #4's Dexterity Saving Throw: 7

The figure strikes at Eldin, but a flare of hellfire strikes back in retaliation. They try and dodge the magic, but fail and get lightly singed in the process. (DCF #4: 4 damage.)

INITIATIVE TRACKER

Ith concentration check: 15

Boo silently darts into the sky coach.

Boo drops onto the party's rented sky coach, Biff appears to be chasing after the opposing one from beneath. "Lucky thing I chose to tail you, right?" He says, seeing Boo land. "Wait, are you shorter than before?"

(Boo's movement was to get onto the sky coach. From this point, the sky coach will assist in helping her catch up.)

Boo shrugs at Biff getting settled in and digging into her pack, "yeah lucky me," and pulls out some items (--bandages, etc.--) from her Healer's Kit 12 and proceeds to make the best use of her time and patches herself up just a bit.

Boo patches herself up with the healer's pack while Biff keeps them on track, accelerating so they can catch up (next round, Boo will be able to fly up to catch up to the DCF's sky coach). (Boo: 31/38 HP)

Everyone else's turns!

INITIATIVE TRACKER