I only saved $40 or so by switching LAX-LHR-LAX to LAX-LHR// CDG-LHR-LAX where the CDG-LHR in on BA. I know I incurred $40 yq from the BA segment, but I thought the difference between UK and France taxes (is it called APD in France) would be more than $80.

Anyone know the APD from CDG? Does $80 difference between CDG and LHR APD sound right?

The French tax de solidarite is less than UK APD, but your connection CDG-LHR-LAX meant you were paying:

French airport taxes
tax de solidarite
LHR airport taxes (but not APD)

From ITA, a business class BA CDG-LHR connecting to AA LHR-LAX:

United Kingdom Passenger Service Charge Departures (UB)
€34.56
USDA APHIS Fee (XA)
€3.38
US Immigration Fee (XY)
€5.96
US Customs Fee (YC)
€4.69
AA YR surcharge (YR)
€178.00
US International Arrival Tax (US)
€15.33
France Passenger Service Charge International (QX)
€12.53
France Civil Aviation Tax Domestic And International (FR)
€8.06
France Airport Tax Domestic And International (FR)
€12.75
France Air Passenger Solidarity Tax (IZ)
€45.07

The passenger would not be paying the AA YR surcharge , but there would be a BA surcharge for the intra EU flight , which istr is about $60 in club europe

Was checking LHR-DFW award in business class and perplexed by the charges

Adult base fare (per passenger) $0.00 USD
US APHIS USER FEE (UNITED STATES) $3.96 USD
US CUSTOMS USER FEE (UNITED STATES) $5.50 USD
US FEDERAL INSPECTION FEE (UNITED STATES) $7.00 USD
AIR PASSENGER DUTY (APD) (UNITED KINGDOM) $193.70 USD
PASSENGER SERVICE CHARGE (UNITED KINGDOM) $53.50 USD
Total $263.66 USD

If APD $193.70?
When I checked ITA matrix for a similar flight, it show APD as GBP75 = USD97.
Where did the extra $100 come from?

Ba fuel charges for award tickets are different than what they are on a revenue ticket.

APD for business class is GBP150, which at the moment is approximately $193.70

I assume that you were checking for economy class on ITA

My bad....yes, I was looking at economy class.

Am I crazy or is IB no longer showing up in searches for award tickets in AA.com?

I don't know if all IB award flights do not show. But I found 2 J seats ob the ORD-MAD IB nonstop for July 17 2017 on both the QF and BA award search sites. It does not show on the AA award search.

Does South America get some sort of exemption on the BA charges? On the aa.com site booking a business class award GRU-LHR-MAD (BA>IB) the total fees are $60usd + 87,500 miles.

Adult base fare (per passenger) $0.00 USD
EMBARKATION TAX (BRAZIL) $35.40 USD
PASSENGER SERVICE CHARGE (UNITED KINGDOM) $24.60 USD
Total $60.00 USD

There is , iirc, a prohibition by the Brazil government on surcharges

Even on normal bookings for GRU-LHR , the taxes are a total of BRL114.97 ( approx USD35.50 )

Ibera is starting non-stop service SFO-MAD in April 2018. I looked for a business class seat and put it on hold.

I can't believe this: Carrier Imposed Fees: $478.00.

I looked for non-stop Iberia service from other airports. Much, much less. For example: LAX-MAD: Carrier Imposed Fees: $82.30.

This is mad! Does anyone think that this is an error? Maybe because it's new service? Any thoughts about this?

It is in line with what the other IAG airline, BA, charges

It maybe an error and it will drop in line with other routes or it could just be where IB is moving its charges to and the others will come in line

How about booking SFO-LAX-MAD?

Yes, I am looking into that. There's not much availability though.