Karax by SpectralDuke

Level 1:
W-Attuned Targeting: Phase Cannons deal an additional 50% damage to non-heroic targets.
E-Fire at Will: Quest. Hitting enemy heroes with Orbital Strike increases the damage of Orbital Strike by 1. Reward: Hit 30 enemy heroes with Orbital Strike to reduce its cooldown by 2 seconds.
D-Solar Core Refinement: Quest. Gathering a Regeneration Globe grants 2 Solarite. Gather 25 Regeneration Globes to generate an additional 1 Solarite every 3 seconds.

Level 4:
Q-Temporal Mirage: Using Chrono Beam on an allied hero grants them a stack of Block, reducing damage from the next hero basic attack they take by 75%.
D-Fortification Barrier: When an allied target is damaged near a Shield Battery, that target immediately gains a shield equal to 10% of their maximum health for 5 seconds. This effect has a 20 second cooldown.
Observer: 50 second cooldown. Karax gains the ability to warp in cloaked Observers which reveal an area. Observers are destroyed in 1 basic attack or if hit by ability damage, and Karax can only have 3 Observers active at once.

Level 7:
E-Advanced Munitions: Orbital Strike's area is increased by 25%.
D-Enhanced Targeting: All of Karax's structures, including his Phase Cannons, have their range increased by 20%.
D-Repair Drones: Karax's drones can now repair allied structures while nearby at a rate of 1% of the structure's maximum health every 3 seconds.

Level 10:
R-Master Phase-Smith
R-Solar Lance

Level 13:
Q-Phased Out: Using Chrono Beam on an allied hero makes them Resistant for 2 seconds.
W-Forge Efficiency: Phase Cannon gains an additional charge.
D-Adamant Construction: Karax's structures take 10% less damage while their shields are down.

Level 16:
Q-Chrono Rush: Chrono Beam now grants 30% attack and movement speed to its target.
Q-Chrono Boost: Chrono Beam increases its target's health and mana regeneration by 100% and their basic ability cooldowns recharge 100% faster.
D-Optimized Ordnance: Photon Cannons, Phase Cannons and Khaydarin Monoliths attack 25% faster.
E-Phase Detonation: Enemies hit by Orbital Strike are stunned for 0.3 seconds.

Level 20:
R-Unity Barrier: All allied units and structures gain a shield equal to 10% of their maximum health. Once depleted, this shield is restored after 60 seconds.
R-Solar Flare: Solar Lance's cooldown is reduced by 5 seconds and it sets the target area ablaze for 10 seconds, burning enemies inside it for 43 (+4% per level) damage per second.
Chrono Overload: Activate to increase the attack speed of all allied units and structures by 50% for 10 seconds. 100 Solarite, 90 second cooldown.
Khalai and Templar: Karax's attacks deal an additional 20% damage and give him a shield equal to 20% of the damage dealt for 5 seconds.

Quotes:

Selection Screen:
My expertise is yours!

Game Start:
"Make no mistakes. I am Khalai and Templar both."
"Let us engineer victory."
"Ah, Hierarch. It is good to fight beside you." (to Artanis)
"Is it truly the great Tassadar? I-I am not prepared..." (to Tassadar)

Heroics:
"Spear of Adun, clear this point!"
"Activating Solar Lance!"
"Purifying the area!"

"I am activating Chrono Boost now!" (Chrono Overload)

Thoughts:
Karax is an interesting hero because of his dual role, with his storyline in LotV having him begin as an engineer who through circumstance becomes a warrior. I decided to reflect this by giving him two paths he can take, either focusing on his structures and very much being about shoring up defenses and creeping forward with Cannons, Batteries and Monoliths, or tooling him for direct combat with his Chrono Beam talents and others. I did decide to let Enhanced Targeting and Optimized Ordnance work on his Phase Cannons to give those talents some use in direct combat build. His heroics are meant to emphasize his dual role, with Master Phase-Smith making him tower defense extraordinaire and letting him heal up all your structures, while Solar Lance is a big flashy teamfight ultimate that does a lot of damage.

For the ultimate upgrades, Solar Flare was just a simple cooldown reduction plus adding the burning ground effect, and I went with Unity Barrier for the Master Phase-Smith upgrade because it fit tower defense Karax's passive playstyle while still supporting his team. Chrono Overload is a support ability that works for either Karax since it also works on structures, and Khalai and Templar is ironically for direct combat Karax to give him some punch and sustain.

The way his structures work if replacing destroyed ones is that they aren't targeted by the objectives on Sky Temple and Blackheart's Bay, and Khaydarin Monoliths replacing your destroyed Keeps don't stop catapults spawning (Illarian and Beleth, Punishers, and the Zerg on Braxis will still target down Karax's structures). I was tempted to have the AI map objectives ignore his structures, but it seemed weird to have them just run past a Monolith that's shooting them in the face.

Numbers specifically might need some tweaking, not sure if he or his structures are under or over tuned.