Re-routing and AE reward
 

I scored a pretty good AE First Class one-way reward as follows:

TG I class SIN-BKK
TG O class BKK-ICN
OZ O class ICN-LAX
AC I class LAX - YYZ ( lie flat)

If I wanted to further optimize this, say by flying SIN-ZRH/MUC/FRA-YYZ
in LX/LH First, if these become available, would I be able to make the change?
Would scam charges be re-calculated?
What if I fly the first leg SIN-BKK, then change to BKK-FRA/ZRH/MUC-YYZ? Again, would
scam charges be recalculated?

Yes, however LX doesn't release any F award availability to partners, and LH no longer operates any flights with a F cabin to YYZ/YUL, so your options are somewhat limited.

Yes.

Very hit and miss IME. The claim that AE never recalculates taxes/fees after departure definitely is not accurate IME.

It certainly does if routing is different in terms of airports. It may not recalculate the scam charges like carrier charge if any are due originally or after itinerary change.