Other people can also get married all you have to do is befriend the bachelor by giving him gifts and one day he will show up and invite you to the wedding. If a girl is at a pink heart you might not see the rival cutscenes. If you are married they will still marry their rival but only after you have been married. They will go through the same process as your wife and have a baby. The costume the baby wears varies by girl and all 5 can be seen below.
There is only 5 couples no one else can get married:
1. Ann & Cliff
2. Elli & Baker
3. Popuri & Gray
4. Karen & Kai (must save vineyard)
5. Harris & Maria
No other couples but these 5 can get married.
I have noticed that if the girls are at pink heart (some have said yellow even) they will not marry their rival at all until you pick your spouse so you don't have to worry about the girl marrying their rival instead of you if you have her heart level at pink.
Now saying that lets saying you didn't have a girl at pink and she is a low heart level and marries the rival, but you change your mind and want to marry her instead the game does allow you to do that see more here.
Ann & Cliff
Elli & Jeff (Baker)
Popuri & Gray
Karen & Kai (must save vineyard)
Harris & Maria