when warhead size increases it derives higher and higher share of its energy from fusion, thus it becomes relatively cleaner and cheaper (per megaton)
Although this claim has popped up before, it isn't strictly true. Whilst there is a lower size limit for a fission device, it isn't necessarily possible to scale up a fission-fusion device to arbitrary sizes without adding additional fissile materials (eg. the U238 tamper or plutonium "sparkplug" in a Teller-Ulam device).
More importantly though, small clean bomb designs not only exist, but have in fact been used. Nuclear weapons were used for peaceful purposes as part of civil engineering works, with varying levels of success and fallout. The three bombs used as part of the Pechora-Kama Canal works were apparently the cleanest ever detonated, with 98% of their yield being from fusion reactions, and they were only 15kt each.
With regards to much larger bombs, note that a substantial proportion of the yield of a Teller-Ulam device can come from the U-238 radiation case and tamper, which is fissioned by the fast neutrons that come out of the D-T reactions in the fusion part of the explosion. In a classic 2-stage design, as much as 50% of the yield of the bomb comes from U-238 fission, and that is gonna yield a non-trivial amount of dirty fallout. The Tsar Bomba test used a lead tamper to reduce yield and fallout, which apparently halved its yield. Still, 50Mt isn't bad...
Additionally, as 80% of D-T and 40% of D-D fusion energy is released in the form of high energy neutrons (and as D-T is the more energetic reaction it is preferred in a weapon, and the neutrons it emits are particularly high energy) you will always get a significant amount of neutron activation in surrounding matter. The amount of radioactive fallout generated by this process, and how long it will last depends very much on what the local landscape is made of. "Safe to walk on after a year" is not the same as "safe to live in" or perhaps more importantly for your use-case, "safe for children to play in and eat dirt because of course they eat a stupid amount of that stuff no matter how hard you try to stop them". The Taiga devices in the Pechora-Kama project produced a significant amount of Cobalt-60 through neutron activation from the fusion neutron flux, much of it from natural ferrous metals present in the soil. With a half-life of >5 years, you may have to wait a while for it to cool down.
Now, bear in mind that the Teller-Ulam design's biggest benefit is the fact that it can be miniaturised to fit in a MIRV warhead. A device intended for landscaping can be arbitrarily large, delicate and complex. You may find that you're able to use other, cleaner ways of producing a big fusion reaction that aren't suitable for weapons. Pure D-D fusion might be possible, and devices with a minimum of metal components (or only ones which don't transmute into dangerous isotopes under neutron bombardment) would be desirable.
Krakatau volcano explosion, equivalent of 200 Mt caused a year without summer, but otherwise Earth climate was fine
Volcanic explosions are not really comparable to nuclear explosions... temperatures are much lower, and energy is released over a longer period of time. I suspect that volcanic explosions will be vastly more effective at moving dirt than nuclear ones. This also makes them much more effective at causing serious climatic changes than nuclear weapons.
Also, don't dismiss the year without a summer. It caused massive worldwide upset causing significant agricultural issues, famine, social problems and polictical upheaval. It wasn't just a bit chilly between spring and autumn.
If placing a nuclear warhead (In 50 Mt range) to cut the mountain top, what would be the shape of "crater"? (Would the cut be roughly flat? Or maybe concave like in normal crater? Or maybe convex, as the sides of the mountain offered less resistance to the explosion?)
You may as well just use a bunch of little warheads scattered around in strategic locations, especially given the existence of small clean bombs. If they're well buried you may find that most of the fallout is contained anyway, and smaller warheads can produce much neater results. Getting a flat mountain top with one big mountain-smasher will be problematic, but a bunch of little ones will produce a post-blast environment that's a bit closer to what you want.
2) For landscaping purposes what would happen to ejecta? (Would it mostly fall in to nearby valley, thus creating some dam? Would it overwhelmingly be spread all over the planet, thus leaving local valley practically unchanged?)
You are in almost complete control over this, especially if you use lots of little warheads. Lots will fall back into the craters or voids left by the bombs exploding. With small enough bombs buried deep enough, you may get very little ejecta at all... lots of big landslides and cliff collapses and so on, but you want the energy to smash the mountain, not fling boulders halfway to the next country.
A bomb powerful enough to spread ejecta all over the world is not suitable for landscaping, and your neighbours (if they exist) will be very unhappy with you.
To follow on from L. Dutch's observation, "I am not that sure that the layer of heavily cracked rocks would make a good substrate to build a city upon" (which is very true), you'll have to spend some time for the debris to settle, and you're gonna want to squish it down and help bind it togther. Getting your heavy construction plant up to the top of a mountain is going to be a slightly larger logistical challenge than merely blowing it up in the first place...