Does the new house need to install a signal amplifier, or is it mandatory to install a signal amplifier?

Whether to add an amplifier or not depends not on the distance of the client, but only on the signal at home. The original 300 meters on the main road plus a first-class power amplifier.

Although you are in the countryside, you also need to transform digital TV. Therefore, every terminal needs a set-top box in the future, and the signal cable TV operator will help you consider it. You only need to install a weak box for each household, and pull coaxial cable and Category 5 cable from the weak box to the point where TV is used, and pull Category 5 cable to the point where computer is used. Remember that the weak box should have power supply. That will do.