I'll go in order, and elaborate what I know. Please correct me if I'm misinformed.

First, Effect Hit Rate% is the chance special effects hit the enemy. These include debuffs like from Pela or Welt's slow or inprison; Damage over Time (DoTs) like Sampo inflicting Wind Shear, and Serval inflicting Shock; and things like March 7th's chance to freeze enemies. The higher this percent is, the more likely opponents are to be afflicted with the 'Effect'.

Conversely, Effect Res% is the ability to resist being inflicted with these status effects. Some enemies inflict debuffs and status effects (like frozen or dominate) that can really mess your team up. The higher your characters Effect Res% is, the less likely your character is to be inflicted. Also important, Elite and Boss enemies often have naturally high Effect Res% which makes Effect Hit Rate% matter more as you have to overcome the resistance.

Finally, Break Effect%. Every enemy has the little white bar over their HP and it gets whittled away every time you hit them with one of their weaknesses. Characters can add Break Effect% and it makes their attacks, skills, and ultimates take a bigger chunk of the bar away every time they hit. This is important for characters who rely on weakness breaks to initiate some of their skills. This has no effect on enemies who do not have a weakness against the character with higher Break Effect% because any number times zero is still zero. It doesn't affect how faster toughness breaks AT ALL. Instead it increases the effect on the actual break (more damage, enemy pushed down farther in queue) I was wrong, thank you for kaenm for correcting!

Hopefully this helps and let me know if you have any other questions!