It seems to be tall and potentially "tippy" for lack of a better term. Does anyone have problems with stability using this?

Good question. I had the same first impression. I don't even have this stove but I think I can give you a better answer than anyone else after studying the pics and thinking about this. In the fully assembled pics, you see two sections: top and bottom. What keeps them together? Well, there's a 3 section (ash can / burn chamber / what holds the wood) nested inside that keeps the top and bottom locked together.

Could I nest a toaks 450ml cup inside this and then place this into a 750ml toaks cup?

You can nest a 450ml cup inside the stove. The stove will not fit in the 750ml pot. It will nest in the 1100ml pot nicely.

Thinking about getting this stove, but what do you do if there is no dry kindling or wood available? Can you use alternate fuel sources, fuel tabs?

1. Alcohol. Just cut the bottom off a can, fill, and light 2. Sticks dry if in a dry pocket during the hike. 3. Cotton balls and Vaseline will easily dry your wood. 4. Fuel tabs burn faster due to better air flow, and will dry your wood. Etc.

can one use a trangia stove in this? How do you get it up to the right height?

The stove was made to be used for biofuel. I have never tried to use any kind of alcohol stoves in this stove. If you probably get it up to the right height it may work.