chemical cell/redox

1. the statement must incorrect!
copper and zinc in solid state, can itself be oxidized to its ion form
Cu --> Cu2+ + 2e- E= -0.34V
Zn --> Zn2+ + 2e- E = + 0.76V
so, we can conclude Zn is a stronger reducing agent than Cu.

but, this doesn;t mean Cu is stronger oxidizing agent than Zn. because Zn and Cu seems attain their highest oxidation number, which is 0. it cannot be further reduced ... So there should have no reduction on Cu or Zn, unless you can make a compound which allow , say Cu2- or Zn3-, etc...

2. the Zn --> Zn2+ + 2e-
when it is not connected by wire, i.e. not discharging, the above reaction will basically not occur. rather, Zn + 2H+ -> Zn2+ + H2 will preferentially reacted.
after connection, the Zn has intention to give up 2e- because the cathode
MnO2 + H+ + 2e- --> H2O + Mn2O3, which is a complete two half equations with E = around + 1.5V , so Zn will just give electron and MnO2 will accept it.

"Ammonium chloride acts as reducing agent."??
the H+ is produced by NH4+ --> NH3 + H+
so... oxidation number did not change...
I doubt this!
if it can be a reducing agent, then it must oxidized, which means level up the oxidation number. oxidation may means lost of electron or gain oxygen atom or lost hydrogen atom. unless it takes the "lost hydrogen atom" as oxidation, thus i think, in oxidation number definition, it can't fulfill the reducing agent meaning!