There are two types of Skills.
Prep Skills Edit
Examples include Light side ATK Up and Dark DEF Down. These Skills only activate randomly, but last through the whole Battle once they activate. Only up to three Skills activate before Battles, regardless of how many Skill Cards you have in your Formation. Skills are determined if they activate or not in the order of highest Skill Grades.
Combat Skills Edit
Combat Skills activate during Battles, unlike Prep Skills. These Skills usually affect Cards in your Formation. Examples include Self ATK Up and 3-Unit All Stats Up. Whether particular Combat Skills activate or not is determined every Turn during Battles, based on the probability assigned for that particular Skill. When they do activate, they last for only that Turn. (These Skills do not stack even when they activate the next turn.) There are no limits to how many Combat Skills can activate per Turn.
Please note though, that when a single unit is in range of two or more of the same skill, only skill is effective on that unit. (Skills with the same name but different activation probabilities ([Sml]/[Med]) are considered DIFFERENT Skills.)