I have been playing horn for 4 years and have at my own opinion improved greatly.
This year for UIL solo & Ensemble I chose to play the second and third movements of Morceau de Concert.
I needed to know the tempo of the adagio section and Allegro non troppo.
I have already played it at the first level,
and played the adagio at about eighth note=60
and the Allegro at about quarter=100
Are these tempos correct?

I don't think you should be too concerned about a "correct" speed. However, I believe the Cantabile needs to go a fraction faster crotchet = 104 - its just too difficult to make it sing any slower. I play the Adagio at quaver=75 which I feel allows more expression in the second half of that section.