There could be a band of Cs climates, but Cfb->BS is also valid. I forgot to mention this the last time, but the same site that includes the Köppen map I previously linked also has some projected climate maps for 2100. Here's one from a high CO2 emission scenario: map. Those might be useful since they reflect a modelled situtation where the Earth is warmer than present.
Other than that, I might remark that a direct Csa->Cfb transition is slightly unrealistic. That is because the Ca/Cb and f/s letters are assigned based on different criteria. To make matters short, Ca/Cb describes the temperature pattern, while f/s describes the precipitation pattern. And of course it's a bit unlikely that the temperature based transition from a to b would 100% match the precipitation-based transition from s to f. It would probably be more likely to have either Csa->Csb->Cfb or Csa->Cfa->Cfb.
Yeah it could well be winter dry if the climate is similarly monsoonal as Asia.
Looks ok to me.
It probably would be f yes (which means there is no distinct dry season btw, not necessarily that there is more rain per se). Dfa->BS is fine, but I would be more concerned about Cfb->Dfa or Cfb->Dfc. You would expect Cfa->Dfa->Dfb or Cfa->Cfb->Dfb for similar reasons as I described under point 1. This also applies to the Cwa->Dfa transition, it would work better as Cwa->Dwa->Dfa.
[Edit: It's also interesting to note that the Tibetan Plateau is projected to develop a Cwb/Dwb/Dwc climate in the "2100 high emission scenario" I linked.]
Yes there should be a desert, the extent of which is basically up to you. It could potentially be larger. The transitions themselves are fine though I think the BS layer between BW and Cs climates should be more narrow, looking at the example of Earth's climates.
Hard to say with certainty. Continental arrangement was one big factor though: the chain of events leading to the present relatively cold climate started when Antarctica parked itself under the South Pole and became completely isolated. The buildup of Antarctic glaciers had a massive long term effect on the climate because it created a region that supplies basically all the world's oceans with their bottom water (colder water being denser and sinking to the bottom), the Antarctic Bottom Water or AABW. This had an effect of making the oceans much colder in the long run.
It's also thought that the CO2 levels in the atmosphere were much higher during the Jurassic, probably at least partially due to the ongoing breakup of Pangaea and the associated volcanic eruptions.