Spectrum auctions, which allow a spectrum owner to sell licenses for signal transmission over specific bands, can allocate scarce spectrum resources quickly to the users that value them most and have received a great deal of research attention in recent years. While enabling reusability-driven spectrum allocation, truthful spectrum auction designs are also expected to provide price fairness for homogeneous channels, online auction with unknown and dynamic spectrum supplies, and bounded system performance. Existing works, however, lack of such designs due to the inherent technically challenging nature. In this paper, we study the problem of allocating channels to spectrum users with homogeneous/heterogenous demands in a setting where idle channels are arriving dynamically, with the goal of maximizing social welfare. Taking spectrum reusability into consideration, we present a suite of novel and efficient spectrum auction algorithms that achieve fair pricing for homogeneous channels, strategy proofness, online spectrum auction with a dynamic supply and a log approximation to the optimal social welfare. To the best of our knowledge, we are the first to design truthful spectrum auctions enabling fair payments for homogenous channels and spectrum reusability with dynamic spectrum supply. Experimental results show that our schemes outperform the existing benchmarks by providing almost perfect fairness of pricing for both single- and multi-unit demand spectrum users.