You can view you relations by pressing [TAB] and choosing heart icon. You can develop friendship with all villagers if you give them gift. You can increase your relations up to 5 heart for normal villagers.
You can view you relations by pressing [TAB] and choosing heart icon. You can develop love relations with only 3 person. Celine, Felicia, Merfit. If you have 5 hearts with romancable character, she will call you a date (cutscenes) and askes you out.
You can gift to all interactable villagers at town. All villagers has like something different. You can learn what they love from them. Each day you can only give 1 gift to each person. If you sleep your gift limit will be reset.
If you increase your relation with, Celine, Felicia, Merfit to 5 heart, they will ask you to meet them with at certain place.
You can accept or decline to be together with them. If you accept your relation status will be updated to "Dating".
If you decline they can be angry or sad but nothing special. They keep going their lives.