We currently live in a semi-detached house as tenants and will also build one ourselves next year. The current house was built in 1989, and the only noise comes from our own half of the semi-detached house (footsteps from the upper floor, washing machine in the basement); from the neighbor, nothing comes except when he is drilling a hole in the shared wall. The internal partition wall is normally constructed as "double." That means each house has a fully functional exterior wall, with about 4cm of air left between them for insulation. This means the insulation to the neighbor is significantly better than between your own rooms.
Of course, it can be somewhat different in the garden. It depends on the plot. We have about 10 meters from table to table between our terrace and the neighbor's. Between them is a bush and a stack of firewood at the neighbor’s place. Even with normal conversations, you only catch fragments or have to really strain to eavesdrop on a conversation. However, I would claim that even in a detached house, curious neighbors can overhear information if they really want to (e.g., having to "accidentally" water the flowers by the fence when the neighbors are outside).
Regarding the changes, you will probably have to speak to the builder once. Only he will be able to tell you what is still feasible and how expensive deeper changes might be.
About the plot: Have yourself informed whether it is a real division or a division according to [WEG]. In the first case, you have no problem because the plot belongs to you alone. In a division according to [WEG], it may be that you have to coordinate with the neighbors.