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Par = 1
Par = PV of coupons + PV of Principal
if coupons are market coupons = swap rate (with several assumptions) (fixed rate)
coupons can be also forward rates (in case of floater)
1=PV of coupons + PV of principal

PV of coupons = 1 - PV of principal

Coupon = forward rate
PV of coupons = Sum(FDF x forward rate)
FDF = Zn = Discount factor (your formula of Zn is wrong...)
Principal = 1

swap is exchange of fixed coupons against floating coupons

PV of fixed coupons = PV of floating coupons

PV of fixed coupons = Sum(FDF x fixed coupon) = fixed coupon x Sum(FDF)

fixed coupon = swap rate = PV of floating coupons / Sum(FDF)