if you make a modern steam installation with a small nuclear reactor or with a thermonuclear reactor, will the efficiency increase?
Yes, efficiency of a static power generating installation can be quite a bit higher, up to 40 - 45 %. This is due to several factors. First they use steam turbines, which are designed to be equivalent to many stages of expansion. Second the turbines are inherently rotating devices, so there's no loss in converting reciprocating to rotational motion. Third and most importantly, the spent steam is recovered and reused. By adding a condenser, the boiler only needs to bring the water up to 100C one time, subsequently it will be returned to the boiler as hot water or even as lower temperature steam.
Steam was used in cars early on, the Stanley Steamer was one of the most famous in the USA.
http://www.stanleymotorcarriage.com/GeneralTechnical/GeneralTechnical.htm The boiler design is perhaps the most important aspect of light transport steam use. Burning solid fuel makes it very difficult to produce steam quickly, and even more importantly, to stop producing power when it is necessary to stop. Burning solid fuel, one's only options should one need to stop for a traffic light or some other obstacle, are to 1) let pressure build up, possibly dangerously, 2) dump steam to the atmosphere, or 3) Smother the fire. A fire that can be quickly modulated and shut off, to conserve water and a boiler with lots of fire/water surface area per unit mass, for rapid steam production, are important design features of a motor vehicle for street use. For something that can travel for long periods without stopping, like a ocean going ship, or a railroad locomotive, these features are less important.
One practical way to use steam might be a smaller engine, coupled to a generator, charging batteries, that power an electric motor for motive power. This is the power strategy used by the locomotives that replaced the steam engines, and is also used in various other applications. It allows the steady optimal condition running conditions that makes steam more efficient, and the electric motor is there to provide the torque for acceleration.
I think what you built is fascinating. Living in an urban environment as I do, steam power is very frowned on. We aren't even allowed to burn wood for heating our houses. But I've always loved the sound and the smooth power of the steam engine.
Another question about your motorcycle. Did the front fork come from a donor machine, and if so what make and model? I don't think I've seen that suspension method before.