a) These terms were coined by the Nazis in the 1920 to retroactively establish their "Third Reich" (also a term coined by them) as a legitimate successor state to those, so the use of either of those names is problematic, when referring to those eras.
b) You're wrong. The "First Reich" in those terms would describe the Holy Roman Empire (lasting from around 800 to 1806), and the Second Reich is the German Empire from the Unification in 1871 to 1918.