Ha! I've done a bit of trip planning for friends and family, the trick is to come up with a skeletal framework that balances sights/activities/experiences and makes logistical sense for a given time frame/budget. But also gives the traveller enough flexibility to fine-tune/customize things as they go. Most of the people I know aren't group tour types.

Mandarin: none of these places is off the beaten track and if stuck, you'll probably locate someone who can at least speak Me Tarzan You Jane type of English. Take a phrasebook to fall back on, and you'll manage well. Western tourists will be fewer this time of year, but not non-existent. You are more likely to meet other travellers in hostels and guesthouses...many of which have private rooms not just dorms. If you don't need lots of amenities or luxury, consider going this route. Often solo travellers meet up serendipitously and end up doing a day or so (or longer) activities together.

Tickets: Yes, you should be able to buy with just a few days notice, without having to set all dates in advance. Especially air tickets. Air tickets can be bought in any city for any other city pair connection. The only city pair on your itinerary that has limited capacity is Kunming-Guilin (surprisingly), there are few daily flights. You can always go by train but it will take 24 hours and you'll head either south via Nanning or north via Guizhou province--if you have time, either of these directions could make for an interesting stopover for a day or so enroute to Guilin.

Train tickets can only be bought in the city the train is departing from. Hard sleepers will sell out before soft sleepers, as most Chinese are thrifty. On an overnight train, you need a sleeper. (Daytrains for short trips need only a seat). My advice is upon arriving in a new city, make your exit plans and get the train ticket for the next destination then. If your schedule is flexible, then you can be more relaxed, as being stuck for an extra day in a place due to lack of immediate train tickets isn't an issue. However, if you need to meet a schedule deadline on the back-end, then reliability of obtaining a specific train ticket on a specific date may be more important. However, if trains are sold out, you can always throw a little more cash at the situation and fly. In China, there's always a way to resolve any of these logistical things. Again, you can save time for sightseeing by throwing more cash at the problem and upon arriving at your lodging, tell them what you need and let them get the ticket and bring it back to you. I've generally only been charged about RMB 20-30 "service fee" on top of the actual ticket price (hostels and Chinese hotels up to 3*), and to me, I'd rather spend the hour or so of my time to things other than logistic arrangements.