it does stack with Ashe's frost shot, as well as with all other slows, and lizarbuff.
However it does not stack addatively.

Don't remember what frost shots slow percentage is, or at what level.
Lets just say its 50% for easy maths

30% from frozen mallet + 50% frostshot does not = an 80% slow.

Frost shot slows with half, that means that when the FM slow takes effect, the target is already at half speed. which means FM only slows half as much of the targets movespeed.
Which means FM + FS = a 65% slow.
And this effect stacks with every slow in the game, but you will never be able to slow the target a 100%

Adding a lizarbuff on top of that means you slow more than 65% but not much. Since the lizarbuff slows like 30% or something, that means it is first reduced by half, and then by another 70%, meaning you don't get that much out of stacking slows.
So if you have these three slows on an enemy, don't use exhaust for the slow, its a waste.

Stacking slows does however get useful when the target is using abilities to increase their speed.
I am not sure about the exact mechanics, but essentially a frozen mallet pretty much nullifies the buff they gain from using ghost, allowing other slows, like Frostshot to be much more effective when the target has a speed boost.

Does the slow work with a Tiamat?
Do you get an AoE slow or is the slow weaker for the splashed units or does it only work on the guy you are hitting?

Reference :
1HP = 2.6g
1AD = 36g

Stats costs : 2540
Price of effect : 710g

How well, if at all, does this work with Ashe's Frost Shot?

it reduces MS by a different percent if you are ranged or melee. it reduces it by more if you are melee. the slow works similiarly to the lizard buff (red buff).

It's 30%.

reduceds movement.
but by how many %?

joa is ganz töfte