For the same scope, another type of floating stone "on water" would be also fine.
Can that type of stone be used as castle material to float on water? Will it have a different effect if built on salt water and normal water?
Feel free to suggest more appropriate floating stone (real stone if possible) for castle material, if pumice is not good.
I doubt it. Pumice may float if it is thrown into the water, and pumice rafts can get pretty large, but they are not stable enough to build on them. The same would apply to any other floating stone.
There have been concrete ships, but these use air-filled spaces for buoyancy, and concrete as a hull material.
Wood is better construction material.
If you want to build a large, floating base on water, your best bet would be wood. Compared to pumice, wood is more durable and far easier to work with. Your entire structure will be flexing as it moves in the water, and you need something both strong and elastic to absorb the strain of that movement. Pumice is neither.
Pumice does have the advantage of being fireproof. However, even if you're with fire resistance as a major concern, you'd be better of constructing the portion of your castle below the water line out of wood, and then either stacking pumice on top of your floating wooden base or using it as cladding to fireproof an otherwise wooden superstructure.
The closest analogs for "floating castles" are warships like the Spanish galleons. They were big, durable, difficult to attack, and capable of defending key pieces of land. Such ships were built almost entirely out of wood, until metallurgy progressed to the point where they could be first covered in metal, and then constructed entirely out of metal in the manner of modern warships; relying on air-filled cavities for buoyancy, rather than intrinsic properties of their building materials.
I believe you could use pumice to build a floating island, but not really a castle.
Pumice comes as relatively small rocks, so you have to get them to stay together.
Some fancy modern concrete can probably do it. But: the larger the structure, the more stress will the waves put on it, so you will need more or stronger concrete, and probably steel reinforcement. So you are essentially building an oil platform, but with pumice-filled concrete instead of metal tanks for flotation.
If you are limited to medieval/fantasy technology, you will have to stuff pumice rocks into nets or baskets, then tie them together into rafts (maybe with wooden beams to provide more structure), then build whatever you can on top of them. I doubt a large rigid structure can survive ocean waves, so you can have a flexible raft with smaller walls and outposts around the perimeter.
And if I mayb get a bit more creative, maybe you can have some kind of a plant with extensive root system that holds pumice stones together. Maybe some crawling vines, maybe even a tree. The nutrient would have to come from the water, so either float in some inner sea and tap into whatever rivers bring down, or have a ecosystem of fish living in the roots, so tree gets nutrients from their poop.
You know how in various fantasy computer games the castles get destroyed by a bunch of little guys running up to it and hitting it with their swords? That doesn't work brilliantly in real life because the sorts of stone you might build a castle with are fairly strong. Pumice, on the other hand, is pretty straightforward to carve with more or less any tool and a little brute force. You could lay siege to it with a bunch of guys with bouyant shields... paddle out to the castle on your shield, then swim up to the wall underneath it and start chipping away.
In fact, given its soft nature and relatively high-friction surface, there's a reasonable chance that a person could scale a pumice wall armed with crampons and steel picks, as if they were an ice climber. That makes your castle very vulnerable to stealthy swimmers at night.
"But!" I imagine you saying. "I could clad my castle with smooth, hard stone blocks, like a real castle!" well, maybe. Only in order to bouy up the weight of a real castle, you'll need a truly colossal foundation of pumice, and the whole enterprise becomes astonishingly unwieldy. You can't have your pumice extending too far down underwater relative to its width or you'll get stability issues (eg. your castle will topple over in poor weather, because floaty-up, sinky-down is a more stable configuration), so you'll really be making a huge, flat pumice island with a little stone tower in the middle. Have a think about how useful that will be. Next, have a think about how you'll move it around, and not be at the mercy of the elements.
Now you're left with a huge artificial island that's going to be extremely hard to manoeuvre, big enough that it will be easily seen coming, and with a tiny fortification in the middle. What on earth is it going to do? It can't realistically protect or attack anything. It might be a cool place for a wizard to live, but that's about it.
There's no better alternative stone, by the way, if you want to use a lighter-than-water construction stone, it is gonna end up looking a lot like pumice because that density has to be shed somewhere.
The obvious answer as suggested elsewhere, is wood, because it is known to work well. If you were wedded to minerals as a fortification material and were prepared to have a slightly more unusual (eg. somewhat implausible) tech level, there's always concrete-hulled boats as a possibility...
