Why do we prefer germanium over silicon as a semi-conductor?
Not everyone prefers germanium because it has a low melting point which can damage germanium devices when they are soldered into circuits (unless some preventive safeguards are taken). This same property renders them more easily damaged in power handling applications. The good points about germanium are its high electron mobility which makes it a relatively good conductor, and germanium junction devices (transistors & diodes) have a lower forward bias voltage than do silicon junction devices.
Which is better conductor silicon or germanium and why?
Actually both are semiiconductors. These do not have free valence electrons. Due to temperature, free electrons are created. But this fraction is very low. so dopping is performed to make these usable devices with usable conductivities. now for your question, if we are considering these as conductors, germanium is better that, its temperature dependence is high. It creates more freee electrons than silicon at the same temperature and so germanium is more conductive. This is the reason for its rfeduced usage in ICs.