Waalaikum salam
Although genetically risky, cousin marriage is permissible in Islam because cousin is not mahram. But, not every family can approve it. There are families that approve cousin marriage, there are families that do not approve cousin marriage.
Then if a girl likes a guy?. Women is not in position that propose marriage. If a woman has interest to a man she should not propose marriage, directly or through third party, because it's considered inappropriate in mostly cultures. But there is a way that women can do, send an 'invitation' to the men, and very suggested through thrid party that can send this 'invitation' subtly and covertly. In example, the third party seek a chance to chat with the guy and then tell him "Eh, bro, I notice that girl likes you. So, if you are looking for a wife, why not her?". In this matter if the guy like the girl too he would start to take an action. If not? then it could cause an awkward situation when they meet each other.
It's normal if you like someone. But it doesn't mean he must be likes you too. Even if a guy and a girl like each other, there is still possibility they can't get married.
So, young sister, if you like someone, you must be able too to accept the destiny if it turns out he is not for you.