The correct translation for "however" in this case is actually "tuy vậy" and not "tuy nhiên". Rarely do we use the equivalent of "however" to start a sentence in Vietnamese, but when we do, it would mostly translate to "tuy vậy" because "tuy nhiên" can't be used to start a sentence, it's only used to connect two phrases together (if you want the sentence to be grammatically correct).

Our team sucks. However, if we have you, we'll win! = Đội chúng mình tệ. Tuy vậy, nếu chúng tôi có bạn, chúng ta sẽ thắng!

He's quite fast, however, he's still just 12, he couldn't outrun Mike = Nó rất nhanh, tuy nhiên (tuy vậy) nó chỉ mới 12 tuổi, nó không thể chạy thắng Mike.

In a way, "tuy vậy" present contradictions/oppositions, while "tuy nhiên" only present oppositions with an obvious/predictable outcome. In other word, "tuy nhiên" is a sub class of "tuy vậy" and can only be used in specific instance while "tuy vậy" can be used anywhere to present an opposition.

no. I don't know how to explain but it doesn't.