Firstly, the number of domain dots a cultivator may have is capped at one fourth of the cultivators highest cultivation level, rounded down. Ling Qi, whose level is 7, may thus have at most one dots in domain, until she raises one of her cultivation levels to 8.
Each dot of domain gives the cultivator three 'slots' in addition to a baseline of two which can be used to gain bonuses when completing certain arts in addition to improving or expanding abilities which are already locked in. Abilities chosen to fill these slots are PERMANENT, and cannot be changed without significant effort and certain rare resources, abilities which complement or stack with one another will be more potent than more scattered bonuses.
Not all arts grant domain abilities on mastery. No art which completes before the third realm will do so, and even among those that do, only ones which fit the user may grant bonuses. At the beginning, with a mostly 'blank' domain most third realm arts will offer these bonuses, but as you progress, choice will become narrower.