I have always had a doubt, or maybe I didn't read the paper very clearly

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I have always had a doubt, or maybe I didn't read the paper very clearly
I browsed through Wikipedia, but I still can't understand how the size of the p-value affects the results. If possible, please help me answer the following questions:

Can I directly look at the Prob. result to determine the similarity between two proteins?
If so, what reference range should I use? <0.3? >0.6?
If not, what other comparison results should I focus on? Seq. Id? E-Value? Also, in Wikipedia, what is the score compared to the p-value? Is it TM-score?