俺 means “I” in a manly way.
と is the particle used to name things one by one. It used to be attached to each word you name, so in this case it’s supposed to be 俺と西宮と but an omission of the one in the end has become more common in the modern language. It can be used multiple times such as 卵と牛乳とバターとパンを買った meaning “I bought eggs, milk, butter and bread”.
西宮 is the last name of the girl. Japanese people usually don’t use the pronoun “you” especially あなた as it sounds unfriendly, instead, they tend to call a person by their name. You usually call them by their surname when you have a certain distance like if you two just met or they’re just your colleagues, and you start calling them by their first name when you get closer.
友達 means “friends”.
なれる is the potential form of the verb なる meaning “to become”. With a noun, the particle に is usually used so 友達になれる means “can become friends“.
かな is used in questions when you don’t want to sound too assertive. So if it’s 友達になれる？ meaning “can we be friends?” it’s just a simple and direct question for the speaker to get the answer. But by adding かな in the end, you can make it more subtle and humble as it sounds like “Do you think we can be friends?” or “I wonder if we can be friends?”