1. The derivation of Schwarzschild metric using the freely falling frame is discussed in detail in M Visser, 2003, Heuristic approach to the Schwarzschild geometry; gr-qc/0309072.
2. For a textbook discussion, see T Padmanabhan, An Invitation to Astrophysics, World Scientific, 2006.
3. The effective potential as well as orbits in Schwarzschild metric are discussed in any standard text in general relativity, C W Misner, K S Thorne and J A Wheeler, Gravitation, Freeman, ch.25, 1973.