Most highwing cabin types will require considerable down thrust and yes this is normal. If your airplane did not have that downthrust it would require even more down thrim power on.

Also remember most trainers use tail decaledge arrangements that are optimum for level flight at around half power. All power changes with any conventional aircraft will require retrimming for hands off flight every time a power change is made, this is also normal. A sudden power increase will cause the nose of the airplane to pitch up as will a sudden power reduction will cause the nose to drop. The down thrust will soften this pitch up effect when power is suddenly applied but will not totally eliminate it.

John