Friendships
Rosa is a very likeable character, showing a great deal of empathy for everyone involved. For this reason, she befriends everyone who joins the party. Although she never really has the opportunity to meet some of the other characters, it's likely she would befriend them as well.
Signifigant Friendships
Rydia
After Rosa first meets young Rydia, she becomes a mentor of sorts to the young girl. Rosa is always encouraging her when she's sad or upset. She helps Rydia overcome her fear of fire at Mt. Ordeals. Later on, when Rydia returns from the Land of the Summoned Monsters Rosa is shocked that she had grown up. Throughout the rest of the game, Rosa and Rydia form a close friendship, being the two females in the party. They even plot together in order to come along with Cecil and the others to the moon despite what Cecil commanded of them.
Kain
During childhood, it's likely that Kain and Rosa knew eachother for some time before they met Cecil. Over time, Kain grows to harbor feelings toward Rosa, yet he keeps them inside. However, there are several points where these feelings are evident in the way that he regards Rosa. In the end, he feels horrible for betraying them both. This leads to him going to Mt. Ordeals to overcome his guilt and to become a better Dragoon. He misses their wedding for this reason. It can be implied that he can't bear to see the woman he loves marrying someone else who she rightfully deserves.
Cid
Rosa has known Cid for most of her life. In a lot of ways, Cid is almost like an adoptive uncle to her. He cares a lot about her, obviously by the quote he gives Cecil at the beginning of the game:
"Rosa's been worried sick about you, you know! Make that girl cry and you'll have me to answer to, you hear?"
Cid later says that he wishes he could stick around to see their children as he is ready to jump to his presumed death. After discovering that Cid is indeed alive, Rosa is overjoyed.
Edge
Rosa certainly feels for Edge, especially when he loses his parents due to Dr. Lugae's experiments. At first, especially evident in the original version of the game, Edge is definitely taken by Rosa's beauty at first
"Two charming girls! Maybe this won't be so bad after all!"
However, it becomes apparent that Cecil and Rosa share feelings with one another. At which point, he focuses his romantic energies on Rydia.