differences between 非常好 and 特别棒 ALSO if I know someone's name, do I 认识 them?
The first question is very confusing. I do not agree that the answer has to be C or D. With only the information you gave us, I can only rule out answer E 天津队的水平比沈阳对高得多. Since Shenyang beat Tianjin 5:1, then Shenyang has to be playing at a much higher level than Tianjin. Other than that, we don't know how good Team Shenyang really is, unless we know how good, or bad a team Team Tianjin is. It is possible that Tianjin is a really, really bad team, and any mediocre team can beat them 5:1. Without further context, all four answers A B C D are possible.
The second question is much better. 认识 is to know personally. Knowing just the name doesn't count. I know the names of a lot of celebrities, but I know very few personally. I cannot say 我認識他們，only 我知道他們的名字。
Having said that, the second question is also a little bit confusing. A says：“我不太了解她”。 This means A doesn't know her well. But does that necessarily mean he does not know her at all? Personally, I would never say “我不太了解她” about someone I do not know at all.
Sorry if I managed to confuse the OP further. Without more context, these questions are just not clear and fair for the learner.