You made a good point with the runes and masteries, i will change it thanks.
The thing about the Hextech is the additional nuke lets you kill carries almost instantly together with your other skills. Also you get pretty high attack and spellvamp very early.
It works for me atleast.
I might wanna swap out the force of nature for abyssal scepter, because i feel like i have enough regen with hextech. Void staff is still a good choice as your skills scale pretty badly with AP and much better with magic pen. I tried zhonyas and a void staff did more damage most of the time for less money.
Rylais scepter does only a 35% slow if you Q attack someone solo or ult.
I feel like i have enough slow with randuins and hextech, i mean they can easily be wasted thats for sure
but if you use them wisely its more than enough.
I dont like dorans shield and will stay with regrowth pendant because it lets me spam skills thus having my iron man up all the time and farm pretty good. Dorans shield might be a good choice for a sidelane tho.

Thanks for your long detailed comment i appreciate it :)

Defensive masteries are a waste on him imo. You spend 5 mastery points for only 2% dodge chance and a 10% movespeed bonus when you dodge. Those masteries are only worth it if you get dodge runes and/or ninja tabi. You spend another 4 mastery points for a meager 60 hp.

On Mord, it's much better to go for a 9/0/21 mastery build. This nets you a very nice 9% cd reduction at lv 1- 14.89% with your runes. You get the experience mastery which helps you level faster. You get the movement speed mastery which gives you a nice boost that syngerizes well with the movespeed quints you chose. You should also take the ghost mastery and presence of the master as these will allow you to use ignite and ghost much more often. Obviously you want to skip the mana related masteries in utility.

As for runes, hp regen seals pale in comparison to hp/lv seals. Regen is arguably the worst stat in the game. Having extra health will go much further to increase your regen anyways because it will increase the regen you get from force of nature. For the quints, I usually go for flat hp, but movespeed are viable as well. However, it makes much more sense to get movespeed quints along with the movespeed utility mastery.

Your item build is decent, however, I think gunblade is a bit of a waste on him. I think a Rylais Scepter would be much better. Even though his q bounces, I'm pretty sure you still get the 35% slow from it. You get a 15% slow aura with his w and you get a nice 35% slow added to his ult each time it ticks damage. As a bonus, you can also give your carry a slow aura by casting w on him as he chases down an enemy. Void Staff is a situational item that you should pass on unless the enemy team is stacking magic resist against you. In place of that, I would recommend a Zhonyas Ring for the added survivability. If you really want more magic pen, consider picking up an Abyssal Scepter.

As for the starting item, I usually go with a Doran's Shield. The amount of stats you get for the gold is completely unmatched early game. It allows me to lane almost indefinitely and only recall when I want to. Along with the +hp/lv seals and +hp quints you end up with a ridiculous amount of hp early game.

Like i already explained AD doesn't contribute to his passive.

If you go Ap/tank you still have lots of survivability through your abilities which
boost your passive.
Your build would make him incredible squishy as he has no slow no CDR only one defensive item. Mordekaiser isn't a tank but still, that doesn't mean you shouldn't get
defensive items.
A mix between magic and tank seems like the way to get the most out of him.

I've played carrykaisers before, although my build for this is nothing like yours.
dodge runes, tabi, armor/regen armor of choice, Phantom dancer, blood thirster, phantom dancer, blood thirster.

my best carrykaiser score is 29/8/17

Ill gladly answer all the questions you have.
Constructive criticism wanted.

Also try before voting and leave comments if you downvote