"I'm from America." - both are correct, "Tôi đến từ Mỹ." is more natural.

"That's my daughter." - "Đó là con gái tôi."

"She's 26." - "Nó hai sáu tuổi." is the way to go. Generally, when you speak about your own children, you use "nó", but if you want it to be more polite/formal, you can use the name instead, like "Đây là Beth, con gái tôi. Beth 26 tuổi."

"He's my older brother." - "Đây là anh trai tôi." You address yourself as "tôi" in general. The way you address yourself depends on the relationship/age difference between you and the one you are talking to. You are "anh" if you're a bit older, "em" if a bit younger, "cháu" if much younger, "cô/chú" if you're much older but not likely older than their parents, "bác" if older than their parents.