I'm wondering why you won't answer the question about how old she is? You said you're 20. I'm starting to wonder whether she's a minor and now you do realize why this would be an improper relationship based on that fact and that's why you're evading the question.
Oh boy.... I had to Google to see how close "third cousin" is and it turns out... Very. At least where i come from. My dad is Montenegrin and there relationship between your relatives us kept so tight that for exampke what is cousin, or 2nd or third cousin we refer to as brother and dister. My family is close with our 4th cousins, and guess what... We also refer to them as... Distant sidter, or brother or aunt. It wss practically impossible for anyone to develop any erotic or romantic feelings there because ever since you've known them you never looked at them that way and the sole notion of seeing my 3rd cousin that wsy makes me feel... Iffy. I know that marrying into the family happens in the West as well as east and even though it is legal in my native country it's highly frowned upon. So much so that I've never even heard of any such case.
Now about your case, don't you think that maybe she's being nice to you cause she sees you as her family. And how old is this girl mind my asking? I'm just trying to put myself in her shoes and if anyone who's related to me told me they like me... Romantically that would freak me out. Yet again i come from quite different upbringing.
I have to be honest. You sound like a lonely person with very limited experience. Is there a reason you never have dated? It would then make sense that you grow a major crush on a young woman that is kind, friendly, warm to you because you are helping to tutor her and are family. You are most likely misinterpreting this and her behavior. I don't know your age. her age. And truthfully none of this sounds like a good idea.
I should ask for a little clarification, too.
First of all, I had been assuming you were past the age of majority, not a teenager, and are able to support yourself. Are you?
I also read this (since you were taking about love) as, (should your third cousin once removed be interested), you would want to ask her to marry you.
If you are not that old yet, or if you are not really that sure, then please do not consider making any kind of move or dropping any kind of hint. :) Before age 24 or 25, well -- we do change our minds as we grow up, after all. You don't want to fall into disrepute over something that you later realize was transitory.
You know, this could end badly. I'm not sure 'how' close you truly are family wise. She's your third cousin's daughter . . . what does that make her to you. However, you refer to her as family and know your third cousin as family so then this is implying that your family may have an issue with it. Is it worth a big broo ha ha in the family? You've basically got a crush. Those are not real life romance. Just means you are interested. I guess you can send out some subtle hints and see what she says. But decide if it is worth a major issue if it blows up. good luck
In many countries, a third cousin once removed is not considered taboo to marry. Are you certain this is so where you are? If society would shun you, then you have to keep your interest to yourself.
It might merely be awkward in some countries for someone to be romantically interested in a (somewhat distant) relative, but awkwardness is not enough to stop true love, if it is true love. (If you are just talking about lust, forget ever telling her or anyone else, and cool your jets.)
If you somehow manage to find out that she returns your regard, and if your intention is marriage, the familial connection between the two of you should not be enough of a roadblock to refrain unless there are societal punishments. That said, if everyone from her mother on up and down the family tree would be shocked and horrified, then I am afraid you do have to refrain from even telling your cousin of your feelings.
Also, if you think there is a chance she herself would be appalled and frightened, don't tell her. You do not want to look like a harasser to her. In such a situation, enjoy the friendship and be glad you get that much.