Does the Bride give the Sister of the Groom a gift?

No, that’s not traditional unless she’s a bridesmaid.

You don't have to.

but if she's a part of your wedding like a reader or helping out in general, etc or just has done a lot for you for the wedding then it would be nice!

Gifts to the parents are NOT traditional, beyond giving them an album or framed pictures after the wedding. There has been a recent trend of giving everybody gifts every time you turn around, but parents are celebrated with gifts on their birthdays, their anniversary, Mother's Day, Father's Day, and winter holidays with presents, but not on your wedding day.
You can do what you want. But traditionally this is time for them to give you a wedding gift.

Not necessary unless she's a bridesmaid. Parent gifts are optional too.

I will be, only because they are bridesmaids. If they weren't in the wedding party I wouldn't be

Nope! It’s normal to give gifts to the bridal party and parents, but that’s where it ends. The presents are thank you gifts for their help, support, and in the case of parents, for raising you.

No, it's not tradition but you may do so at your discretion.

If she's in your wedding party, I'd say yes. If she's not officially part of the wedding, I don't think it's necessary but would be a nice gesture. Maybe a necklace or bracelet that says something about being your "bonus sister" or "sister by choice".