What it a player has the ball in the front court. He dribbles to the division line and touches but does not go over the line, with his foot. Is this considered a backcourt violation?

Yep.

4-13-2

The division line is in the BC.

"The lines are not considered part of the court."
Step on the line you're OOB, step on the 3p line, you're shooting for 2, step on the middle line, you're in the BC
so yeah, violation, in FIBA also if you dribble the ball on the line you're in the BC

I've heard this put slightly differently.
All the OOB lines are out, all the lines in the court are in.

Meaning if you step on an OOB line you are OUT of the playing court, but if you step on any other line you are inside of that area. Some examples: step on a FT lane line and you are inside the FT lane, step on the 3 pt line and you are inside the 2 pt area, step on the division line and you are in the backcourt, step on the center restraining circle and you are inside the circle, and step on the OOB line while executing a throw-in and you are STILL OOB.