All following has been carried out in free play.
Challenge 1: Go at Least 180 mph on Homestead Miami.
My 1st try was 10 laps of the speedway track with an Indy Car.
It did not register at all.
My 2nd try was 2 laps of same track with 2015 McLaren P1 GTR.
It worked.
Challenge 2: Complete 6 laps of Daytona.
My 1st try was 6 laps of the speedway track with 2015 McLaren P1 GTR.
It did not register at all.
My 2nd try was 7 laps of same track with an Indy Car.
It worked.
Challenge 3: Complete 3 races in a Forza P1 Division Car.
My 1st try was 2017 Porsche 919 Hybrid on 1 lap of Homestead.
I did quit after the first race, and it did not look like registering ( 0/3 ).
For my 2nd try, I took Daytona speedway, and went for a reasonable number of 4 laps.
When I did quit, it had registered ( 1/3 ) although I had not scored a win.
For Race nº2, I kept the same car, same race.
I did not quit, and left it to the game to sort the 3rd, and I ran 3 laps on the GP Nurburgring.
It worked.
Challenge 4: Wina race in a HyperCar Division car.
I ran 3 laps of Top Gear Outer Loop, forward, in a McLaren P1 GTR.
It registered.
ALL this is NOT a solution.
These are just what worked and didn't for me.
Hope this helps.
Update 1:
Although the Challenge popped and is registered on Xbox & TA,
The Forzathon line does not completed in the game, and I have not received the car.
To be followed.
Update 2:
As mentioned by other players, if you come back later on in the game, you should find the forzathon challenge completed, and a message gifting you the car.