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There are threads in the forum devoted to both of these topics.
1. Other people are mentioning the same thing, that there seems to be a mismatch in opponent strengths. There is no good work-around (aside from shutting off network connections to get an easier opponent) other than figuring out a bird team that can deal with most opponents you face, so that you can cycle through the ones that you know beat you more often than not.
2. No conclusion was reached on whether or not the coin flip is fair. Tracking wins/losses in some cases suggests it is biased. However, the evidence was not completely persuasive and some people remain convinced it is fair, and the negative bias observes (more losses of the flip than wins) is simply due to a small sample size.