Is there a way to change game modes and settings on current saved games?

Modes, I am sure no. Settings, depending on what you are asking, maybe no, but sometimes yes. Difficulty setting, no. But the check box to hide/show detailed horse stats does work on existing games.

If it was an option you selected when you started that save file, no. Like schedule, difficulty, legends.

If it was an option off the game launcher screen (before you pick a save), then usually yes. Like showing stats, weight measurement units.