Horses are best able to answer our aids when they are clear, with no confusing background noise! What does that mean for us as riders? It means that we need to strive to begin each aid from a state of complete neutrality. A clean slate. Learn all about it here.
Practicing transitions on a circle allows you to utilize the bend and increased engagement from the circle to improve the connection in your transitions.
"In every sport, life goes in waves, up and down, keep rowing the boat and you’ll meet the next wave coming up, but don’t jump out of the boat!" ~ Chris Bartle
To make your seat stronger when seated in the saddle, think of using your core muscles in a downward fashion.
Horses need to be honestly connected and on the aids before they can stretch properly over their entire topline. Without that connection from behind, the stretch will be the horse's neck only, which is far less productive than a real stretch over the back.